UNIVERSITY   OF  CALIFORNIA. 

Received. 
Accessions 


ON  &  CO. 
Stationers 


ELEMENTS 


OF 


NATURAL  PHILOSOPHY. 


A    TEXT-BOOK 


FOR    HIGH     SCHOOLS    AND    ACADEMIES. 


BY 


ELROY    M.   AVERY,   PH.D., 

M 
AUTHOR    OF    A    SERIES    OF    PHYSICAL    SCIENCE    TEXT-BOOKS. 


ILLUSTRATED    BY   MORE.  THAN  400  WOOD    ENGRAVINGS. 


SHELDON     ANDCOMPANY, 

NEW    YORK    AND    CHICAGO. 


DR.     AVERY'S 
PHYSICAL    SCIENCE     SERIES 


'St. 

FIRST     PRINCIPLES     OF     NATURAL     PHILOSOPHY, 

9*. 

THE    ELEMENTS    OF    NATURAL    PHILOSOPHY. 


THE     ELEMENTS     OF     CHEMISTRY. 

4th. 
THE    COMPLETE    CHEMISTRY. 


This  contains  the  ELEMENTS  OF  CHEMISTRY,  with  an  additional  chapter  on 
Hydrocarbons  in  Series  or  Organic  Chemistry.  It  can  be  used  in  the  same  class 
with  THE  ELEMENTS  OF  CHEMISTRY. 


Copyright^  1878,  1885,  by  Sheldon  &  Company. 


Klectrotyped  by  SMITH  A  McDoUGAL, 
82  Beekman  St.,  New  York. 


CHAPTEK    I. 

THE     DOMAIH     OF     PHYSICS. 

PAGE 

SECTION  I. — The  Domain  of  Physics 1 

II.— The  Properties  of  Matter 6 

"     III.— The  Three  Conditions  of  Matter 21 

CHAPTEE    II. 

D  Y  N  A  MICS. 

SECTION  I. — Force  and  Motion 25 

"       II.— Gravitation 46 

"     III.— Falling  Bodies 57 

"     IV.— The  Pendulum 69 

"       V.— Energy 76 

CHAPTER    III. 

SIMPLE     MACHINES. 

SECTION  I.— Principles  of  Machinery  ;  the  Lever 86 

"       II.— The  Wheel  and  Axle  ;  Wheel- work  97 

"     III.— The  Pulley  ;  the  Inclined  Plane 103 

"      IV.— The  Wedge,    Screw,   Compound    Machines    and 

Friction 109 

CHAPTEE    IV. 

LIQUIDS. 

SECTION  I.— Hydrostatics 116 

"       II. — Liquid  Equilibrium  ;  Capillarity ;  Buoyancy 128 

"     III.— Specific  Gravity 135 

"     IV.— Hydrokinetics .  145 


IV  CONTENTS. 

CHAPTER    V. 

PNEUMATICS. 

PAOH 

SECTION  I. — The  Atmosphere  and  Atmospheric  Pressure 156 

'"        II. — The  Relation  of  Tension  and  Volume  to  Pressure .   163 
"      III.— Air,  Forcing  and  Lifting  Pumps  ;  the  Siphon 168 

CHAPTER     VI. 

ELECTRICITY     AND     MAGNETISM. 

SECTION  I. — General  View 183 

II.—  Frictional  Electricity 192 

"      III.— Voltaic  and  Thermo-Electricity 366 

"      IV.— Magnetism 301 

V.— Induced  Electricity 333 

"      VI.— Electric  Currents  related  to  Heat  and  Mechanical 

Work 353 

CHAPTER    VII. 

SOUND. 

SECTION  I. — Nature,  Refraction  and  Reflection  of  Sound 367 

"       II. — The  Telephone  and  Phonograph — Composition  and 

Analysis  of  Sounds 384 

CHAPTER    VIII. 

H  EAT. 

SECTION  I.— Temperature,  Thermometers,  Expansion 412 

"        II. — Liquefaction,  Vaporization,  Distillation 424 

"      III.— Latent  and  Specific  Heat 436 

"      IV.— Modes  of  Diffusing  Heat 450 

V.— Thermodynamics 462 

CHAPTER    IX. 

LIGHT. 

SECTION  I.— Nature,  Velocity  and  Intensity  of  Li^ht 475 

II.— Reflection  of  Light 483 

"      III.— Refraction  of  Light , 500 

IV. — Chromatics  and  Spectra 516 

"        V. — Optical  Instruments  and  Polarization 534 

CONCLUSION  ;  ENERGY 552 

APPENDICES 561 

INDEX..  584 


TO     THE    TEACHER. 


IN  this  book  will  be  found  an  unusual  number  of  prob 
lems.  It  is  not  intended  tbat  each  member  of  each 
class  shall  work  all  of  the  problems.  It  is  hoped  that 
they  are  sufficiently  numerous  and  varied  to  enable  you 
to  select  what  you  need  for  your  particular  class.  No 
author  can  make  a  comfortable  Procrustean  bedstead. 

You  would  do  well  to  secure,  in  the  fail  of  the  year,  a 
supply  of  the  pith  of  elder  or  sunflower  stalk,  and  several 
full-blown  thistle-heads,  that  they  may  be  well  dried  and 
ready  for  experiments  in  electricity  during  the  dry,  cold 
weather  of  winter. 

The  author  would  be  glad  to  receive  any  suggestions 
from  any  of  his  fellow- teachers  who  may  use  this  book,  or 
to  answer  any  inquiries  concerning  the  study  or  apparatus. 

Most  of  the  apparatus  mentioned  in  this  book  may 
•  be  obtained  from  JAMES  W.  QUEEN  &  Co.,  Philadelphia. 

The  author  has  prepared  a  Teacher's  Hand-Book  to 
accompany  this  volume,  with  answers  to  the  problems, 
and  much  additional  matter  of  interest  to  teachers  of 
Natural  Philosophy. 


TO    THE    PUPIL. 


EECENT  easeful  and  extended  examination  shov/fc 
1  that  diseases  of  the  eye,  such  as  near-sight,  are 
lamentably  frequent  among  school-children.  Your  eye- 
sight is  worth  more  to  you  than  any  information  you  are 
likely  to  gain  from  this  book,  however  valuable  that  may 
be.  You  are  therefore  earnestly  cautioned: 

1.  To  be  sure,  in  studying  this  or  any  other  book,  that 
you  have  sufficient  light. 

2.  That  you  do  not  allow  direct  rays  of  light  to  fall 
npon  your  eyes,  and  that  you  avoid  the  angle  of  reflection. 

3.  That  you  avoid  a  stooping  position  and  a  forward 
inclination  of  the  head.     Do  not  read  with  the  book  in 
your  lap.     The  distance  of  the  eye  from  the  page  should 
be  not  less  than  twelve  inches  (30  cm.)  nor  more  than 
eighteen  inches  (45  cm.)     Hold  the  book  up. 

4.  That  you   sit    erect  when  you  write.      The    light 
should  be  received  over  your  left  shoulder. 

5.  Especially,  that  you  avoid,  as  much  as  possible,  books 
and  papers  poorly  printed  or  printed  in  small  type. 

6.  That  you  cleanse  the  eyes  with  pure  soft    watei 
morning  and  night,  and  avoid  overtaxing  them   in  any 
way. 


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THE    DOMAIN    OF    PHYSICS.— THE   PROPERTIES  OF 

MATTER.— THE    THREE    CONDITIONS 

OF    MATTER. 


I. 


THE    DOMAIN    OF    PHYSICS,    OR    NATURAL 
PHILOSOPHY. 

Introductory. — On  the  page  opposite,  you  have  an 
outline  map  of  the  wide  realm  of  human  knowledge.  As 
from  a  mountain  top,  you  look  upon  the  plain  below,  and 
clearly  see  the  position  of  each  province,  and  its  relation 
to  its  neighbors.  Through  some  of  these  provinces  you 
may  have  passed,  and  with  them  have  become  more  or 
less  familiar.  From  the  whole  number  we  now  select  one 
that  promises  enough  of  interest  and  profit  to  justify  the 
time  and  effort  of  careful  study.  Not  satisfied  with  the 
cursory  glance,  we  seek  more  definite  information.  For 
this,  we  must  leave  the  peak  and  enter  the  plain;  for 
though  distance  may  lend  an  enchantment,  it  also  begets  a 
dimness  fatal  to  our  purpose. 

1.  What  is  Science  ?  —  Science  is  classified 
knowledge. 

A  person  may  have  lived  for  years  among  plants,  have 
acquired  a  vast  store  of  information  concerning  them, 


2  THE  DOMAIN  OF  PHYSICS. 

know  that  this  one  grows  only  in  wet  ground,  that  anothe! 
is  valuable  for  such  and  such  an  end,  and  that  a  third 
has  certain  form,  size,  and  color.  This  general  informa- 
tion may  be  valuable,  but  it  is  only  when  the  facts  are 
classified,  and  the  plants  grouped  into  their  respective 
orders,  genera  and  species,  that  the  knowledge  becomes 
entitled  to  the  name  of  botany,  a  science. 

2.  What  is  Matter? — Matter  is  anything  that 
occupies  space  or  "  takes  up  roojn." 

There  are  many  realities  that  are  not  forms  of  matter. 
Mind,  truth,  and  hope  do  not  occupy  space ;  the  earth  and 
the  rain-drop  do. 

3.  Divisions  of  Matter. — Matter  may  be  con- 
sidered as  existing  in  masses,  molecules,  and  atoms. 

A  clear  apprehension  of  the  meaning  of  these  terms 
is  essential  to  a  full  understanding  of  the  definition  of 
Physics  as  well  as  of  much  else  that  follows. 

4.  What  is  a  Mass? — A  mass  is  any  quantity 
of  matter  that  is  composed  of  molecules. 

The  word  molar  is  used  to  describe  such  a  collection  of 
molecules. 

(a.)  The  term  mass  also  lias  reference  to  real  quantity  as  distin- 
guished from  apparent  quantity  or  size.  A  sponge  may  be  com- 
pressed so  as  to  seem  much  smaller  than  at  first,  but  all  of  the 
sponge  is  still  there.  Its  density  is  changed  ;  its  quantity  or  mass 
remains  the  same.  This  double  use  of  the  word  is  unfortunate, 
but  the  meaning  in  any  given  case  may  be  easily  inferred  from  the 
connection. 

(6.)  The  quantity  of  matter  constituting  a  mass  is  not  necessarily 
great.  A  drop  of  water  may  contain  a  million  animalcules  ;  each 
animalcule  is  a  mass  as  truly  as  the  greatest  monster  of  the  land  or 
sea.  The  dewdrop  and  the  ocean,  clusters  of  grapes  and  clusters 
of  stars,  are  eqmally  masses  of  matter. 


DOMATN  OF  PHYSICS.  3 

5.  What  is  a  Molecule? — A  molecule  is  the 
smallest  quantity  of  matter  that  can  exist  by  itself. 
It  is  the  physical  unit  of  matter  and  can  be  divided  only 
by  chemical  means. 

(a.)  We  know  that  a  drop  of  water  may  be  divided  into  several 
parts,  and  each  of  these  into  several  others,  each  part  still  being 
water.  The  subdivision  may  be  carried  on  until  we  reach  a  limit 
fixed  by  the  grossness  of  our  instruments  and  vision ;  each  particle 
still  is  water.  Even  now,  imagination  may  carry  forward  the 
work  of  subdivision  until  at  last  we  reach  a  limit  beyond  which  we 
cannot  go  without  destroying  the  identity  of  the  substance,  In 
other  words,  we  have  a  quantity  of  water  so  small  that  if  we  divide 
it  again  it  will  cease  to  be  water  ;  it  will  be  something  else.  This 
smallest  quantity  of  matter  that  can  exist  by  itself  and  retain  its 
identity  is  called  a  molecule.  The  word  molecule  means  a  little 
mass.  (See  A  very 's  Chemistry,  §  4.) 

(&.)  The  smallest  interval  that  can  be  distinctly  seen  with  the 
microscope  is  about  8  Q  jyoiy  inch.  It  has  been  calculated  that  about 
2000  liquid  water  molecules  might  be  placed  in  a  row  within  such 
an  interval.  In  other  words,  an  aggregation  of  8,000,000,000  water 
molecules  is  barely  visible  to  the  best  modern  microscopes. 

6.  What    is    an    Atom  ? — An   atom    is    the 
smallest  quantity  of   matter    that  can   enter   into 
combination.     It  is  the  chemical  unit  of  matter  and  is 
considered  indivisible. 

In  nearly  every  case  an  atom  is  a  part  of  a  molecule. 

(a.)  If  a  molecule  of  water  be  divided,  it  will  cease  to  be  water 
at  all,  but  will  yield  two  atoms  of  hydrogen  and  one  of  oxygen. 
The  molecule  of  common  salt  consists  of  one  atom  of  sodium  and 
one  of  chlorine.  Some  molecules  are  very  complex.  The  common 
sugar  molecule  contains  forty-five  atoms. 

(&.)  Atoms  make  molecules  ;  molecules  make  masses.  Of  the 
absolute  size  and  weight  of  atoms  and  molecules  little  is  known ; 
Df  their  relative  size  and  weight  much  is  known,  and  forms  an  im- 
portant part  of  the  science  of  chemistry. 

7.  Forms   of  Attraction.— Each  of  these   three 
divisions  of  matter  has  its  own  form  of  attraction : 


4  THE  DOMAIN  OF  PHYSICS. 

Molar  attraction  is  called  gravitation. 

Molecular  attraction  is  called  cohesion  or  adhe- 
sion. 

Atomic  attraction  is  called  chemical  affinity  (chem- 
ism).  "'.-•. 

8.  Forms  of  Motion. — Each  of  these  three  divi- 
sions of  matter  has  its  own  form  of  motion  : 

Molar  motion,  or  visible  mechanical  motion,  is  called 
by  different  names  according  to  the  nature  of  the 
substance  in  motion ;  e.  g.,  the  flow  of  a  river  or  the 
vibrations  of  a  pendulum. 

Molecular  motion,  called  heat,  light,  electricity,  or 
magnetism. 

Atomic  motion.     (Purely  theoretical  as  far  as  known.) 

9.  Physical    Science. — Physical   science    com- 
prises Physics  and  Chemistry. 

The  first  of  these  deals  with  masses  and  molecules;  the 
second  with  atoms  and  combinations  of  atoms. 

1C.  What  is  a  Physical  Change? — A  physi- 
cal change  is  one  that  does  not  change  the  identity 
of  the  molecule. 

(a.)  Inasmuch  as  the  nature  of  a  substance  depends  upon  the 
nature  of  its  molecules,  it  follows  that  a  physical  change  is  one  that 
does  not  affect  the  identity  of  a  substance.  A  piece  of  marble  may 
be  ground  to  powder,  but  each  grain  is  marble  still.  Ice  maj 
change  to  water  and  water  to  steam,  yet  the  identity  of  the  sub- 
stance is  unchanged.  A  piece  of  glass  may  be  electrified  and  a 
piece  of  iron  magnetized,  but  they  still  remain  glass  and  iron.  These 
changes  all  leave  the  composition  and  nature  of  the  molecule  un^ 
changed  ;  they  are  physical  changes. 

11.  What  is  a  Chemical  Change  ?— ^  chemi* 


THE  DOMAIN   OF  PHYSICS. 


cal  change   is  one  that  does  change  the  identity 
of  the  molecule. 

(a.}  If  the  piece  of  marble  be  acted  upon  by  sulphuric  acid,  fi 
brisk  effervescence  takes  place  caused  by  the  escape  of  carbonic  acid 
gas  which  was  a  constituent  of  the  marble;  calcium  sulphate 
(gypsum),  not  marble,  will  remain.  The  water  may,  by  the  action 
of  electricity,  be  decomposed  into  two  parts  of  hydrogen  and  one  of 
oxygen.  The  nature  of  the  glass  and  iron  may  easily  be  changed. 
These  change  the  nature  of  the  molecule  ;  they  are  chemical 


±2.  Definition.  —  Physics,  or  Natural  Philos* 
ophy,  is  the  branch  of  science  that  treats  of  the 
laws  and  physical  properties  of  matter,  and  of 
those  phenomena  that  depend  upon  physical 
changes. 

Recapitulation. — To  be  reproduced  and  amplified 
by  the  pupil  for  review. 


Matter. 


PHYSICAL 
SCIENCE. 


PHYSICS... 


Divisions. 

[MASSES. 
MOLECULES 
MULtLULtb> 


Attractions. 
GRAVITATION. 


Motions. 


COHESION- 
ADHESION 


(  Heat. 

-  \    \  Li&ht* 

.  »     1  Electricity. 

[  Magnetism 


(CHEMISM 
OR 
AFFINITY 


THE  PROPERTIES   OF  MATTER. 


ECTfON  H. 


THE    PROPERTIES    OF    MATTER. 

13.  Properties  of  Matter.—  Any  quality  thai 
belongs  to  matter  or  is  characteristic  of  it  is  called 
a  property  of  matter. 

Properties  of  matter  are  of  two  classes,  physical  and 
chemical. 

14.  What  are  Physical  Properties  t— Physi- 
cal   properties    are    such    as    may    be    manifested 
without  changing  the  identity  of  the  molecule  (§  10). 

(a.}  A  piece  of  coal  takes  up  room,  it  is  hard  and  heavy,  it  can- 
not move  itself.  These  several  qualities  or  properties  the  coal  may 
exhibit  and  still  remain  coal,  or  still  retain  its  identity.  They  are, 
therefore,  physical  properties  of  coal. 

15.  What  are  Chemical  Properties  ? — Chem- 
ical Properties  are  such  as  cannot   be  manifested 
without  changing  the  identity  of  the  molecule  (§11). 

(a.)  A  piece  of  coal  may  be  burned  ;  therefore  combustibility  is 
a  property  of  the  coal.  This  property  has  been  held  by  the  coal 
for  countless  ages,  but  it  never  has  been  shown.  Further,  this 
piece  of  coal  never  can  show  this  property  of  combustibility  with- 
out ceasing  to  exist  as  coal,  without  losing  its  identity.  When  the 
coal  is  burned,  the  molecules  are  changed  from  coal  or  carbon  to 
carbonic  acid  gas  (C02). 

16.  Experiment. — Take  a  piece  of  ordinary  sul- 
phur (brimstone)  and  attempt  to  pull  it  in  pieces ;    the 
degree  of  its   resistance  to   this  effort,  or  its  tenacity, 
measures  the  attraction  of  the  molecules  for  each  other. 
Strike  it  with  a  hammer,  and  it  breaks  into  many  pieces, 
thus  manifesting  its  br idleness;  but  each  piece  is  ordinary 


THE  PROPERTIES   OF  MATTER.  7 

sulphur.  Heat  it  in  a  spoon,  and  it  assumes  the  liquid 
form,  but  it  is  sulphur  yet.  In  none  of  these  changes  haa 
the  nature  cf  the  molecule,  or  the  identity  of  the  sub- 
stance, undergone  any  change.  On  the  other  hand,  ii 
the  sulphur  be  heated  sufficiently  it  will  take  fire  and 
burn,  producing  the  irritating,  suffocating  gas  familiar  to 
all  through  the  use  of  common  matches.  We  thus  see 
that  the  sulphur  is  combustible.  This  combustibility  is 
a  chemical  property,  in  the  manifestation  of  which  the 
identity  of  the  substance  is  destroyed.  Before  the  mani- 
festation we  had  sulphur;  after  it  we  have  sulphurous 
anhydride  (SO*).  The  original  molecules  were  elemen- 
tary, composed  of  like  atoms ;  the  resultant  molecules 
are  compound,  composed  of  unlike  atoms,  sulphur  and 
oxygen. 

17.  Division  of  Physical  Properties.— Physi- 
cal properties  of  matter  are,  in  turn,  divided  into  two 
classes,  universal  and  characteristic. 

18.  What  are  Universal  Properties  ?—  Uni- 
versal properties  of  matter  are  such   as  belong  to 
all  matter. 

All  substances  possess  them  in  common ;  no  body  can 
exist  without  them.  We  cannot  even  imagine  a  body 
that  does  not  require  space  for  its  existence.  This  qual- 
ity of  matter,  which  will  soon  be  named,  is,  therefore, 
universal. 

19.  What  are  Characteristic  Properties?— 

Characteristic    properties    of  matter    are    such    as 
belong  to  matter  of  certain  kinds  only. 

They  enable  us  to  distinguish  one  substance  from  an- 


8  THE  PROPERTIES   OF  MATTER. 

other.  Glass  is  brittle,  and  by  this  single  property  may 
be  distinguished  from  india-rubber. 

20.  List  of  Universal  Properties.— The  prin- 
cipal universal  properties  of  matter  are  extension,  im- 
penetrability,    weight,      indestructibility,      inertia, 
mobility,    divisibility,  porosity,  compressibility,  ex- 
pansibility, and  elasticity. 

21.  List  of  Characteristic  Properties. — The 

characteristic  properties  of  matter  (often  called  specific  or 
accessory  properties)  are  numerous.  They  depend,  for  the 
most  part,  upon  cohesion  and  adhesion.  The  most  im- 
portant characteristic  properties  are  hardness,  tenacity, 
brittleness,  malleability,  ductility. 

22.  What  is    Extension? — Extension  is  that 
property  of  matter  by  virtue  of  which   it  occupies 
space. 

.  It  has  reference  to  the  qualities  of  length,  breadth,  and 
thickness.  It  is  an  essential  property  of  matter,  involved 
in  the  very  definition  of  matter. 

(«.)  All  matter  must  have  these  three  dimensions.  We  say  that 
a  line  has  length,  a  surface  has  length  and  breadth  ;  but  lines  and 
surfaces  are  mere  conceptions  of  the  mind,  and  can  have  no  material 
existence.  The  third  dimension,  which  affords  the  idea  of  solidity 
or  volume,  is  necessary  to  every  form  of  every  kind  of  matter.  No 
one  can  imagine  a  body  that  has  not  these  three  dimensions,  that 
does  not  occupy  space,  or  "  take  up  room."  Figure  or  shape  neces- 
sarily follows  from  extension. 

23.  English  Measures. — For  the  purpose  of  com. 
paring  volumes,  as  well  as  surfaces  and  lengths,  measures 
are  necessary.     In  the  United   States  and  England  the 
yard  has  been  adopted  as  the  unit,  and  its  Divisions,  ag 


THE  PROPERTIES   OF  MATTER.  9 

feet  and  inches,  together  with  its  multiples,  as  rods  and 
miles,  are  in  familiar  use.  This  unit  is  determined  by 
certain  bars,  carefully  preserved  by  the  governments  of 
these  two  nations. 

24.  Metric  Measures.— The  international  system 
iias  the  merits  of  a  less  arbitrary  foundation  and  of  far 
greater  convenience.     From  its  unit  it  is  known  as  the 
metric  system.     This  system  is  in  familiar  use  in  most  of 
the  countries  of    continental  Europe  and   by   scientific 
writers  of  all  nations,  and  bids  fair  to  come  into  genera] 
use  in  this  country.    For  these  reasons,  as  well  as  for  its 
greater  convenience,  an  acquaintance  with  this  system  is 
now  desirable,  and  will  soon  be  necessary.     It  has  been 
already  legalized  by  act  of  Congress. 

25.  Definition    of  Meter. — The  meter  was   in- 
tended to  be  forty -millionth  of  the  earth's  meridian 
which  passes  through  Paris,  or  as  the  ten-millionth  of  a 
quadrant  of  such  a  meridian.      It  is  equal  to   39.37 
inches.     Like  the  Arabic  system  of  notation  and  the  table 
of  U.  S.  Money,  its  divisions  and  multiples  vary  in  a  ten- 
fold ratio. 

26.  Metric    Measures  of  Length.  —  Ratio 
=  1  : 10. 

(Millimeter     (mm.)  =          .001  w.—     0.03937  inches 
DIVISIONS.    1  Centimeter     (cm.)    =          .01    m.=    0.3937       " 
[  Decimeter     (dm.)  =          .1      m.=     3.937 

ClNiT.  Meter  (m.)    =        1.       m.=  39.37 

r  Dekameter     (Dm.)-      10.        m.=393.7 

Hektometer    (Hm.)=     100.        w.  =  328  ft.  1  inch. 
MULTIPLES.  < 

I  Kilometer       (Km.)=  1000.        m.=     0.62137  miles 

I  Myriameter    (Jfw.)=10000.        w.=    6.2137 


10  THE  PROPERTIES  OF  MATTER. 

Note. — The  table  may  be  read  :  10  millimeters  make  1 
centimeter  ;  10  centimeters  make  1  decimeter,  etc.  The 
denominations  most  used  in  practice  are  printed  in  italics. 
The  system  of  nomenclature  is  very  simple.  The  Latin 
prefixes,  mitti-,  centi-,  and  deci-,  signifying  respectively 
TnVrr»  T^O>  an(^  iV»  an(^  already  familiar  in  the  mill,  cent, 

2  and  dime  of   U.   S.  Money,  are  used   for  the  divisions, 

3  while  the  Greek  prefixes  deka-,  liekto-,  Tdlo-t  and  myria-, 
'^  signifying  respectively  10,  100,  1000,  and  10000,  are  used 
£  for  the  multiples  of  the  unit.     Each  name  is  accented  on 
E   the  first  syllable. 

o 

27.  Metric    Measures    of   Surface.— 

H  Ratio  =  1 :  1O2  =  1 :  1OO. 

U 

f  Square  millimeter  (sq.  mm.} =0.000001  sq.  m. 
|   DIVISIONS.^  Square  centimeter  (sq.cm.)  =0.0001          " 
[  Square  decimeter    (sq.  dm.)  =0.01  " 

0 

n    UNIT.  Square  meter  (sq.  m.)    =1. 

etc.,  etc. 

U 

2       Note. — The  table  may  be  read :  100  sq.  mm.  =  1  sq.  cm. ; 
S   100  sq.  cm.  =  1  sq.  dm.,  etc.     The  reason  for  tile  change 
8   of  ratio  from  10  to  100  may  be  clearly  shown  by  represent- 
ing 1  sq.  dm.,  and  dividing  it  into  sg.  cm.  by  lines,  which 
shall  divide  each  side  of  the  sq.  dm.  into  10  equal  parts  or 
centimeters. 

28.  Metric    Measures  of  Volume.— 
FlG  z    Ratio  =  1 :  1O3  =  1 :  1OOO. 

f  Cubic  millimeter  (cu.  mm.)  =  0.000000001  cu.  m. 
DIVISIONS.  <  Cubic  centimeter    (cu.  cm.)   =  0.000001  " 

[  Cubic  decimeter    (cu.  dm.)  =  0.001  " 

UNIT.  Cubic  meter  (cu.m.)     =  1.308  cu.  yds. 

etc.,  etc. 

29.  Metric  Measures  of  Capacity. — Ratio  = 

JO.— For  many  purposes,  such  as  the  measurement  of 
articles  usuall}r  sold  by  dry  and  liquid  measures,  a  smaller 
unit  than  the  cubic  meter  is  desirable.  For  such  purposes 


THE  PROPERTIES   OF  MATTER.  11 

the  cubic  decimeter  has  been  selected  as  the  standard, 
and  when  thus  used  is  called  a  liter  (pronounced  leeter) 

f  Milliliter    (ml.)  —      1  cu.  cm.=  0.061022  cu.  in. 
DIVISIONS.     \  Centiliter    (cl.)    =     10     "       =  0.338  fid.  oz. 
[  Deciliter     (dl.)  =  100     "       =  0.845  gill. 

UNIT.  Liter         (1.)     =1000     ••       =  1.0567  liquid  qts. 

f  Dekaliter   (Dl.)  ~     10  cu.  dm.=  9.08  dry  qts. 
MULTIPLES.  -I  Hektoliter  (HI.)  =  100cu.dm.=  2  bu.  3.35  pks. 
[  Kiloliter    (Kl.)  -      1  cu.  ra.  =  26417  gals. 

30.  Comparative  Helps. — It  may  be  noticed  that 
the  m.  corresponds  somewhat  closely  to  the  yard,  which  it 
will  replace.      Kilometers  will  be  used  instead  of  miles. 
The  cu.  cm.  may  be  represented  by  the  ordinary  die  used 
in  playing  backgammon.    The  L  does  not  differ  very  much 
from  the  quart,  or  the  Dl.  from  the  peck,  which  they  will 
respectively  replace.     In  fact,  the  L  is,  in  capacity,  inter- 
mediate between  the  dry  and  liquid  quarts. 

31.  What    is    Impenetrability? — Impenetra- 
bility is  that  property  of  matter  "by  virtue  of  ivhich 
two  bodies  cannot  occupy  the  same  space  at  the 
same  time. 

(a.)  Illustrations  of  this  property  are  very  simple  and  abundant 
Thrust  a  finger  into  a  tumbler  of  water ;  it  is  evident  that  the  water 
and  the  finger  are  not  in  the  same  place  at  the  same  time.  Drive  a 
nail  into  a  piece  of  wood  ;  the  particles  of  wood  are  either  crowded 
more  closely  together  to  give  room  for  the  nail,  or  some  of  them  are 
driven  out  before  it.  Clearly,  the  iron  and  the  wood  are  not  in  the 
same  place  at  the  same  time. 

32.  Experiment. —  Through  one  cork  of  a  two- 
necked  bottle  pass  a  small  funnel  or  "  thistle-tube,"  and 
let  it  extend  nearly  to  the  bottom  of  the  bottle.     Through 


12 


THE  PROPERTIES   OF  MATTER. 


FIG.  a. 


the  other  cork  lead  a  tube  to  the  water-pan,  and  let  it 

terminate  beneath  or 
within  the  neck  of 
a  clear  glass  bottle 
filled  with  water, 
and  inverted  in  the 
water-pan.  See  that 
the  corks  are  air- 
tight; if  necessary, 
seal  them  with  wax 
or  plaster  of  Paris. 
If  a  two-necked  bot- 
tle be  not  convenient, 
substitute  therefor  a 

wide-mouthed  bottle  having  two  holes  through  the  cork. 
The  delivery  tube  is  best  made  of  glass.  It  may  be  easily 
bent  by  first  heating  it  red-hot  in  an  alcohol  or  gas  flame, 
Pour  water  steadily  through  the  funnel ;  as  it  descends, 
air  is  forced  out  through  the  delivery  tube,  and  may  be 
seen  bubbling  through  the  water  in  the  inverted  bottle. 
At  the  end  of  the  experiment,  the  volume  of  water  in  the 
two-necked  bottle  will  be  nearly  equal  to  the  volume  of  air 
in  the  inverted  bottle.  This  clearly  shows  the  impene- 
trability of  air. 

33.  What  is  Weight?—  Weight  is  (as  the  term 
is  generally  used)  the  measure  of  gravity  or  molar  at- 
traction (§  7)  of  which  it  is  a  necessary  consequence. 

(a.)  As  all  masses  of  matter  exert  tins  force,  weight  necessarily 
pertains  to  all  matter ;  but,  in  general  use,  the  term  weight  has 
reference  to  bodies  upon  the  earth.  If  a  body  be  placed  near  the 
earth's  surface  and  left  unsupported,  the  mass  attraction  of  the 
earth  for  each  molecule  in  the  body  will  dww  the  two  together,  and 


THE  PROPERTIES   OF  MATTER.  13 

the  body  is  said  to  fall  to  the  earth.  But  in  this  case  we  have  no 
means  of  measuring  the  force  that  draws  the  two  bodies  together. 
If  now  the  body  be  supported,  the  force  acts  as  before  and  produces 
pressure  upon  the  supporting  substance.  This  pressure  measures 
the  attractive  force  acting  between  the  earth  and  the  body,  and  is 
called  weight.  If  a  second  body  like  the  first  be  placed  beside  it, 
the  mass  attraction  of  the  earth  is  exerted  upon  twice  as  many 
molecules,  and,  reciprocally,  the  attraction  of  twice  as  many  mole- 
cules is  exerted  upon  the  earth;  i.  e.,  the  attraction  has  become  twice 
as  great,  and  the  measure  of  that  attraction,  or  the  weight,  has  been 
doubled. 

(6.)  If  the  same  body  were  upon  the  moon,  its  weight  would  be 
the  measure  of  the  attraction  existing  between  the  body  and  the 
moon.  But  as  the  mass  of  the  moon  is  less  than  that  of  the  earth, 
the  attraction  between  the  body  and  the  moon  would  be  less  than 
that  between  that  body  and  the  earth,  and  the  weight  would  be 
proportionally  diminished. 

34.  English  Measures  of  Weight.— For  the 

comparison  of  weights,  as  well  as  of  extension,  standards 
are  necessary.  In  England  and  the  United  States  the 
pound  is  taken  as  the  unit.  Unfortunately,  we  have 
pounds  Troy,  Avoirdupois,  and  Apothecaries',  the  use  vary- 
ing with  the  nature  of  the  transaction.  As  with  the  yard, 
these  units  are  arbitrary,  determined  by  certain  carefully 
preserved  standards. 

35.  Metric    Measures   of   Weight.  —  Ratio 
=  1 : 10. 

C  Milligram  (mg.)  =  0.0154  grains 

DIVISIONS.     \  Centigram  (eg.}  =     0.1543      " 

[Decigram  (dg.)  =  1.5433      " 

UNITS.  Gram  (g)  =  15.432 

r  Dekagram  (Dg.)  =  0.3527  oz.  avoirdupois, 

I  Hektogram  (Eg.)  =  3.5274    « 

|  Kilogram  (Kg.)  =  2.2046  Ibs. 

I  Myriagram  (Mg.)  =  22.046      "  " 


14  THE  PROPERTIES   OF  MATTER. 

36.  What  is  a  Gram  ?—  A  gram  is  the  weight 
of  one  cu.  cm.  of  pure  water,  at  its  temperature  of 
greatest  density  (4°  0.  or  39.2°  F.).  A  5-cent  nickel  coin 
weighs  5  g. 

EXERCISES. 

1.  How  much  water,  by  weight,  will  a  liter  flask  contain  ? 

2.  If  sulphuric  acid  is  1.8  times  as  heavy  as  water,  what  weight 
Df  the  acid  will  a  liter  flask  contain  ?     '  J  »  6  '  V«n~  « 

3.  If  alcohol  is  0.8  times  as  heavy  as  water,  how  much  will  1250 
cu.  cm.  of  alcohol  weigh  ?         /  u  c  &  '  %  —  r^.-- 

4.  What  part  of  a  liter  of  water  is  250  g.  of  water  ?      '/y 

5.  What  is  the  weight  of  a  cu.  dm.  of  water  ? 

6.  What  is  the  weight  of  a  dl.  of  water? 


37.  What  is  Indestructibility?  —  Indestructi- 
bility is  that  property  of  matter  by  virtue  of  which 
it  cannot  be  destroyed. 

(a.)  Science  teaches  that  the  universe,  when  first  hurled  into  space 
from  the  hand  of  the  Creator,  contained  the  same  amount  of  matter, 
and  even  the  same  quantity  of  each  element,  that  it  contains  to-day. 
This  matter  has  doubtless  existed  in  different  forms,  but  during  all 
the  ages  since,  not  one  atom  has  been  gained  or  lost.  Take  carbon 
for  instance.  From  geology  we  learn  that  in  the  carboniferous  age, 
long  before  the  advent  of  man  upon  the  earth,  the  atmosphere  was 
highly  charged  with  carbonic  acid  gas,  which,  being  absorbed  by 
plants,  produced  a  vegetation  rank  and  luxuriant  beyond  comparison 
with  any  now  known.  The  carbon  thus  changed  from  the  gaseous 
to  the  solid  form  was.  in  time,  buried  deep  in  the  earth,  where  it 
has  lain  for  untold  centuries,  not  an  atom  lost.  It  is  now  mined  as 
coal,  burned  as  fuel,  and  thus  transformed  again  to  its  original 
gaseous  form.  No  human  being  can  create  or  destroy  a  single  atom 
of  carbon  or  of  any  other  element.  Matter  is  indestructible. 
Water  evaporates  and  disappears  only  to  be  gathered  in  clouds  and 
condense  and  fall  as  rain.  Wood  burns,  but  the  ashes  and  smoke 
contain  the  identical  atoms  of  which  the  wood  was  composed.  In  a 
different  form,  the  matter  still  exists  and  weighs  as  much  as  before 
the  combustion. 

38.  What    is    Inertia?  —  Inertia  is  that  prop- 
erty of  matter  by  virtue  of  which  it  is  incapable 


THE  PROPERTIES   OF  MATTER.  15 

of  changing  its  condition  of  rest  or  motion,  or  the 
property  by  virtue  of  which  it  has  a  tendency  when  at 
rest  to  remain  at  rest,  or  when  in  motion  to  continue  in 
motion. 

(a.)  If  a  ball  be  thrown,  it  requires  external  force  to  put  it  in  mo- 
tion; the  ball  cannot  put  itself  in  motion.  When  the  ball  is  passing 
through  the  air  it  Las  no  power  to  stop,  and  it  will  not  stop  until 
some  external  force  compels  it  to  do  so.  This  external  force  may 
be  the  bat,  the  catcher,  the  resistance  of  the  air,  or  the  force  of 
gravity.  It  must  be  something  outside  the  ball  or  the  ball  will  move 
en  forever.  Illustrations  of  the  inertia  of  matter  are  so  numerous 
that  there  should  be  no  difficulty  in  getting  a  clear  idea  of  this 
property.  The  "  running  jump "  and  "dodging"  of  the  play- 
ground, the  frequent  falls  which  result  from  jumping  from  cars  in 
motion,  the  backward  motion  of  the  passengers  when  a  car  is  sud- 
denly started  and  their  forward  motion  when  the  car  is  suddenly 
stopped,  the  difficulty  in  starting  a  wagon  and  the  comparative  ease 
of  keeping  it  in  motion,  the  "  balloon"  and  "  banner"  feats  of  the 
circus-rider,  etc.,  etc.,  may  be  used  to  illustrate  this  property  of 
matter. 

39.  Experiment. — Upon  the 
tip  of   the  fore-finger  of  the  left 
hand,  place  a  common  calling-card. 
Upon   this  card,  and  directly  over 

the  finger,  place  a  cent.     With  the  — — ... 

nail  of  the  middle  finger  of  the 
right  hand  let  a  sudden  blow  or  "  snap  "  be  given  to  the 
card.  A  few  trials  will  enable  you  to  perform  the  experi- 
ment so  as  to  drive  the  card  away,  and  leave  the  coin 
resting  upon  the  finger.  Repeat  the  experiment  with  the 
variation  of  a  bullet  for  the  cent,  and  the  open  top  of  a 
bottle  for  the  finger-tip. 

40.  What  is  Mobility  I—Mobility  is  that  prop- 
erty of  matter  by  virtue  of  which  the  position  of 
bodies  may  be  changed. 


16  THE  PROPERTIES   OF  MATTER. 

(a.)  A  body  is  any  separate  portion  of  matter,  be  it  large  or  small, 
as  a  book,  a  table,  or  a  star.  The  term  is  nearly  synonymous  with 
mass,  but  has  not  so  distinct  a  reference  to  the  absolute  quantity  of 
matter.  Bodies  or  masses  are  composed  of  molecules  ;  molecules 
are  composed  of  atoms. 

(6.)  On  account  of  inertia,  the  body  cannot  change  its  own  posi- 
tion  ;  on  account  of  mobility  any  mass  of  matter  may  be  moved  if 
sufficient  for,ce  be  'applied.  This  changing  of  position  is  called 
motion  ;  motion  presupposes  force.  (See  §  64.) 

41.  What  is  Divisibility? — Divisibility  is  that 
property  of  matter  by  virtue  of  which  a  body  may 
be  separated  into  parts. 

(a.)  Theoretically,  the  atom  is  the  limit  of  divisibility  of  matter. 
Practically  the  divisibility  of  matter  is  limited  before  the  molecule 
is  reached  ;  our  best  instruments  are  not  sufficiently  delicate,  our 
best  trained  senses  are  not  acute  enough  for  the  isolation  or  percep- 
tion of  a  molecule.  Nevertheless,  this  divisibility  may  be  carried 
to  such  an  extent,  by  natural,  mechanical  (physical)  or  chemical 
means,  as  to  excite  our  wonder  and  test  the  powers  of  imagination 
itself.  It  is  said  that  the  spider's  web  is  made  of  threads  so  fine 
that  enough  of  this  thread  to  go  around  the  earth  would  weigh  but 
half  a  pound,  and  that  each  thread  is  composed  of  six  thousand  fila- 
ments. A  single  inch  of  this  thread  with  all  its  filaments  may  be 
cut  into  thousands  of  distinct  pieces,  and  each  piece  of  each  fila- 
ment be  yet  a  mass  of  matter  composed  of  molecules  and  atoms. 
The  microscope  reveals  to  us  the  existence  of  living  creatures  so 
small  that  it  would  require  thousands  of  millions  of  them  to  aggre- 
gate the  size  of  a  hemp -seed.  Yet  each  animalcule  has  organs  of 
absorption,  etc. ;  in  some  of  these  organs  fluids  circulate  or  exist. 
How  small  must  be  the  molecules  of  which  these  fluid  masses  are 
composed  !  What  about  the  size  of  the  atoms  which  constitute  the 
molecules  ?  A  coin  in  current  use  loses,  in  the  course  of  a  score  of 
years,  a  perceptible  quantity  of  metal  by  abrasion.  What  finite 
mind  can  form  a  clear  idea  of  the  amount  of  metal  rubbed  off  at 
each  transfer  ? 

42.  What  is  Porosity? — Porosity  is  that  prop- 
erty  of   matter  by    virtue  of   which    spaces  exist 
between  the  molecules. 


THE  PROPERTIES   OF  MATTER.  1? 

(a.)  When  iron  is  heated,  the  molecules  are  pushed  further  apart, 
the  pores  are  enlarged,  and  we  say  that  the  iron  has  expanded.  If 
a  piece  of  iron  or  lead  be  hammered,  it  will  be  made  smaller,  because 
the  molecules  are  forced  nearer  together,  thus  reducing  the  size  of 
the  pores.  Cavities  or  cells,  like  those  of  bread  or  sponge,  are  some= 
times  spoken  of  as  ''sensible  pores,"  but  these  are  not  properly  in- 
eluded  under  this  head. 

43.  What  is  Compressibility  ? — Compressibil- 
ity is  that  property  of  matter  ~by  virtue  of  which 
a  body  may  be  reduced  in  size. 

44.  What  is  Expansibility?— Expansibility  is 
that  property  of  matter  by  virtue  of  which  a  body 
may  oe  increased  in  size. 

(a.)  Compressibility  and  expansibility  are  the  opposites  of  each 
other,  resulting  alike  from  porosity.  Illustrations  have  been  given 
under  the  head  of  porosity.  Let  each  pupil  prove  by  experiment 
that  air  is  compressible  and  expansible. 

45.  What    is    Elasticity? — Elasticity   is   that 
property  of  matter  by  virtue  of  which  bodies  resume 
their    original  form    or   size   when    that  form   or 
size  has  been  changed  by  any  external  force. 

(a.)  All  bodies  possess  this  property  in  some  degree,  because  all 
bodies,  solid,  liquid  or  aeriform,  when  subjected  to  pressure  (within 
limits  varying  with  the  substance),  will  resume  their  original  size 
upon  the  removal  of  the  pressure.  The  amount  of  compression  mat- 
ters not  except  in  the  case  of  solids.  It  was  formerly  thought  that 
liquids  were  incompressible  ;  hence  aeriform  bodies  were  called 
elastic  fluids,  while  liquids  were  called  non-elastic  fluids.  But  the 
compressibility  and  perfect  elasticity  of  liquids  having  been  shown, 
the  term  "non-elastic  fluid"  involves  a  contradiction  of  terms  and 
would  better  be  dropped.  Fluids  have  no  elasticity  of  form  ;  on 
the  other  hand,  all  fluids  have  perfect  elasticity  of  size.  What 
properties  of  matter  are  illustrated  by  the  action  of  the  common 
pop-gun  ? 

46.  What  are  Cohesion   and  Adhesion?— 

Cohesion  is  the  force  that  holds  together  like  mole- 


18  THE  PROPERTIES   OF  MATTER. 

cules;    adhesion   is  the  force  that    holds    together 
unlike  molecules. 

(a.)  Cohesion  is  the  force  that  holds  most  substances 
together  and  gives  them  form.  Were  cohesion  suddenly 
to  cease,  brick  and  stone  and  iron  would  crumble  to  finest 
pIG  powder,  and  all  our  homes  and  cities  and  selves  fall  to 
hopeless  ruin.  In  aeriform  bodies,  cohesion  is  not  ap- 
parent, being  overcome  by  molecular  repulsion  (heat).  In 
large  masses  of  liquids  the  cohesive  force  is  overcome  by  gravity, 
which  tends  to  bring  all  the  molecules  as  low  as  possible  and  thus 
renders  their  surfaces  level.  But  in  small  masses  of  liquids,  the 
cohesive  force  predominates  and  draws  all  the  molecules  as  near 
each  other  as  possible,  and  thus  gives  to  each  mass  the  spheroidal 
form,  as  in  the  case  of  the  dew  or  rain-drop.  Globules  of  mercury 
upon  the  hand  or  table,  and  drops  of  water  upon  a  heated  stove,  are 
familiar  illustrations  of  this  effect  of  cohesion  upon  small  liquid 
masses.  But  in  the  solid  state  of  matter,  cohesion  shows  most 
clearly.  Cohesion  acts  only  at  insensible  (molecular)  distances.  Let 
the  parts  of  a  body  be  separated  by  a  sensible  distance,  and  cohesion 
ceases  to  act ;  we  say  that  the  body  is  broken.  If  the  molecules  of 
the  parts  can  again  be  brought  within  molecular  distance  of  each 
other,  cohesion  will  again  act  and  hold  them  there.  This  may  be 
done  by  simple  pressure,  as  in  the  case  of  wax  or  freshly-cut  lead ; 
it  may  be  done  by  welding  or  melting,  as  in  the  case  of  iron.  Cir- 
cular plates  of  glass  or  metal,  about  three  inches  in  diameter,  often 
have  their  faces  so  accurately  fitted  to  each  other  that,  when  pressed 
together,  a  considerable  force  is  needed  to  separate  them.  (See 
Fig.  4.) 

(6.)  Adhesion  is  the  force  that  causes  the  pencil  or  crayon  to  leave 
traces  upon  the  paper  or  blackboard,  and  gives  efficacy  to  paste, 
glue,  mortar  and  cements  generally.  In  a  brick  wall,  cohesion  binds 
together  the  molecules  of  the  mortar  layer  into  a  single,  hardening 
mass,  while  on  either  hand  adhesion  reaches  out  and  grasps  the  ad- 
joining bricks  and  holds  them  fast— a  solid  wall.  Like  cohesion,  it 
acts  only  through  distances  too  small  to  be  measured  ;  unlike  cohe- 
sion, it  acts  between  unlike  molecules. 

47.  What  is  Hardness? — Hardness  is  that 
property  of  matter  by  virtue  of  which  som,e  bodies 
resist  any  attempt  to  force  a  passage  between  their 
particles. 


THE  PROPERTIES   OF  MATTER.  19 

It  is  measured  by  the  degree  of  difficulty  with  which  it 
is  scratched  by  another  substance.  Fluids  are  not  said  to 
have  hardness. 

(«.)  Hardness  does  not  imply  density.  The  diamond  is  much 
harder  than  gold,  but  gold  is  four  times  as  dense  as  diamond. 

48.  What  is  Tenacity  ? — Tenacity  is  that  prop- 
erty of  matter  by  virtue  of  which  some  bodies  re- 
sist a  force  tending  to  pull  their  particles  asunder. 

(a.)  Like  hardness  and  the  other  characteristic  properties  of 
matter,  it  is  a  variety  of  cohesion  which  is  the  general  term  for  the 
force  which  holds  the  molecules  together  and  prevents  disintegration. 
The  tenacity  of  a  substance  is  generally  ascertained  by  shaping  it  in 
the  form  of  a  rod  or  wire,  the  area  of  whose  cross-section  may  be 
accurately  measured.  Held  by  one  end  in  a  vertical  position,  the 
greatest  weight  which  the  rod  will  support  is  the  measure  of  its 
tenacity.  For  any  given  material,  it  has  been  found  that  the  tenacity 
is  proportioned  to  the  area  of  the  cross-section  ;  e.  g.,  a  rod  with  a  sec- 
tional area  of  a  square  inch  will  carry  twice  as  great  a  load  as  a 
rod  of  the  same  material  with  a  sectional  area  of  a  half  square  inch; 
a  rod  one  decimeter  in  diameter  will  carry  four  times  as  great  a  load  as 
a  similar  rod  five  centimeters  in  diameter.  The  explanation  of  this  is 
simple  ;  imagine  these  rods  to  be  cut  across,  and  it  will  be  evident 
that,  on  each  side  of  the  cut,  the  first  rod  will  expose  the  surfaces 
of  twice  as  many  molecules  as  will  the  second,  and  that  the  third 
will  expose  four  times  as  many  molecular  surfaces  as  the  fourth. 
But  for  the  same  material,  each  molecule  has  the  same  attractive 
force.  Doubling  the  number  of  these  attractive  molecules,  which 
is  done  by  doubling  the  sectional  area,  doubles  the  total  attractive 
or  cohesive  force,  which,  in  this  case,  is  called  tenacity ;  quadru- 
pling the  sectional  area  quadruples  the  tenacity.  Hence  the  law  : 
Tenacity  is  proportioned  to  the  sectional  area. 

49.  What  is  Brittleness? — Brittleness  is  that 
property  of  matter  by  virtue  of  which  some  bodies 
may  be  easily  broken,  as  by  a  blow. 

(a.)  Glass  furnishes  a  familiar  example  of  this  property.  The 
idea  that  brittleness  is  the  opposite  of  hardness,  elasticity  or  tenac- 
ity, should  be  guarded  against.  Glass  is  harder  than  wood?  but 


•THE  PROPERTIES   OF  MATTER. 


very  brittle  ;    it  is  very  elastic,  but  very  brittle  also.     Steel  is  fa* 
more  tenacious  than  lead,  and  far  more  brittle. 

50.  What    is    Malleability  t—  Malleability   is 
that  property  of  matter  by  virtue  of  which  some 
bodies  may  be  rolled  or  hammered  into  sheets. 

(a.)  Steel  has  been  rolled  into  sheets  thinner  than  the  paper  upon 
which  these  words  are  printed.  Gold  is  the  most  malleable  metal, 
and,  in  the  form  of  gold  leaf,  has  been  beaten  so  thin  that  282,000 
sheets,  placed  one  upon  the  other,  would  measure  but  a  single  inch 
in  height. 

51.  What    is    Ductility  ?—  Ductility   is   that 
property  of  matter  by  virtue  of  which  some  bodies 
may  be  drawn  into  wire. 

(a.)  Platinum  wire  has  been  made  3^^  of  an  inch  in  diameter. 
Glass,  when  heated  to  redness,  is  very  ductile. 

52.  Experiment.  —  Heat  the  middle  of  a  piece  of 
glass  tubing,  about  six  inches  long,  in  an  alcohol  flame, 
until  red-hot.     Roll  the  ends  of  the  glass  slowly  between 
the  fingers,  and  when  the  heated  part  is  soft,  quickly  draw 
the  ends  asunder.    That  the  fine  glass  wire  thus  produced 
is  still  a  tube,  may  be  shown  by  blowing  through  it  into  a 
glass  of  water,  and  noticing  the  bubbles  that  will  rise  to 
the  surface. 

Recapitulation.  —  To  be  reproduced  and  amplified 
by  the  pupil  from  memory. 


f  CHEMICAL 

PROPERTIES! 
OF  MATTER.  I 

PHYSICAL. 


GENERAL 


ISTIC. 


Extension,  Impenetrabil- 
ity, Weight,  Indestruc- 
tibility, Inertia,  Mobil- 
ity, Divisibility,  Po- 
rosity, Compressibility, 
Expansibility,  Elas- 
ticity. 

f  Hardntss. 
Tenacity. 
Brittlentss. 
Malleability 
Ductility. 


f  ADHESION. 
! 

I  COHESION. 


THE    THREE    CONDITIONS    OF   MATTER. 


ECTION  HI. 


THE  THREE    CONDITIONS   OF  MATTER. 

53.  Conditions   of  Matter. — Matter  exists  in 
three  conditions  or  forms— the  solid,  the  liquid, 
find  the  aeriform. 

54.  What  is  a  Solid  ? — A  solid  is  a  body  whose 
molecules   change   their    relative    positions    with 
difficulty. 

Such  bodies  have  a  strong  tendency  to  retain  any  form 
that  may  be  given  to  them.  A  movement  of  one  part  of 
such  a  body  produces  motion  in  all  of  its  parts. 

55.  What   is   a   Liquid? — A  liquid  is  a  body 
whose  molecules  easily  change   their  relative  po- 
sitions, yet  tend  to  cling  together. 

Such  bodies  adapt  themselves  to  the  form  of  the  vessel 
containing  them,  but  do  not  retain  that  form  when  the 
restraining  force  is  removed.  They  always  so  adapt  them- 
selves as  to  have  their  free  surfaces  horizontal.  Water 
is  the  best  type  of  liquids. 

56.  Experiment. — Sus- 
pend a  glass  or  metal  plate, 
of    about  four    inches    area, 
from  one  end  of  a  scale-beam, 
and    accurately    balance    the 
same  with  weights  in  the  oppo- 
site scale-pan.     The  support- 
ing cords  may  be  fastened  to 

the  plate  with  wax.    Beneath  FIG.  5. 


THE  THREE  CONDITIONS  Of 


the  plate  place  a  saucer  so  that  when  the  saucer  is  filled 
with  water  the  plate  may  rest  upon  the  liquid  surface,  the 
scale-beam  remaining  horizontal.  Carefully  add  small 
weights  to  those  in  the  scale-pan.  Notice  that  the  water 
beneath  the  plate  is  raised  above  its  level.  Add  more 
weights  until  the  plate  is  lifted  from  the  water.  Notice 
that  the  under  surface  of  the  plate  is  wet.  These  mole- 
cules on  the  plate  have  been  torn  from  their  companions 
in  the  saucer.  The  weights  added  to  the  original  coun- 
terpoise were  needed  to  overcome  the  tendency  of  the 
water  molecules  to  cling  together. 

Note  to  the  Pupil.  —  After  seeing  a  physical  experiment,  always  asb 
yourself,  "  What  was  the  object  of  that  experiment?  What  does  H 
teach?"  Never  allow  yourself  to  look  upon  an  experiment  as  being 
simply  entertaining  ;  thus  reducing  the  experimenter,  so  far  as  you 
are  concerned,  to  the  level  of  a  showman. 

57.  What  is  an  Aeriform    Body?  —  An  aeri- 
form body  is  one  whose  molecules  easily  change 
their  relative  positions,  and  tend  to  separate  from 
each  other  almost  indefinitely. 

Atmospheric  air  is  the  best  type  of  aeriform  bodies. 

58.  Gases    and   Vapors.  —  Aeriform  (having  the 
form  of  air)  bodies  are  of  two  kinds,  gases  and  vapors. 
Gases  remain  aeriform  under  ordinary  conditions,  although 
they   may   be    liquefied   by   intense    cold   and    pressure. 
Vapors  are  aeriform  bodies  produced  by  heat  from  sub- 
stances that  are  generally  solid   or  liquid,  as  iodine  or 
water.     They  resume  the  solid  or  liquid  form  at  ordinary 
temperatures. 

59.  Changes  of  Condition.  —  The  same  substance 
may  exist  in  two  or  even   three  of  these  forms.     Most 


TffREE   CONDITIONS   OF  MATTE&. 

solids,  as  lead  and  iron,  may  be  changed  by  heat  to  liquids ; 
others,  as  iodine,  may  be  apparently  changed  directly  to 
vapors ;  still  others,  as  ice,  may  be  easily  changed  first  to 
the  liquid,  and  then  to  the  vapor  form.  It  is  probable  that 
any  solid  might  be  liquefied  and  vaporized  by  the  applica- 
tion of  heat,  and  that  the  practical  infusibility  of  certain 
substances  is  due  to  our  limited  abilities  in  the  production 
of  heat. 

(a.)  Many  vapors  and  gases,  as  steam  and  sulphurous  anhydride 
(SO 2, the  irrespirable  gas  formed  by  burning  sulphur), may  be  liquefied 
by  cold,  the  withdrawal  of  heat.  The  process  is  one  of  subtraction. 
A  still  further  diminution  of  the  heat  force  would,  in  many  cases, 
lead  to  a  solidifying  of  the  liquid.  It  is  probable  that  all  gasea 
might  be  liquefied  and  all  liquids  solidified,  if  we  had  the  power  of 
unlimited  withdrawal  of  heat.  In  fact,  the  last  of  the  "  permanent 
gases"  has  been  liquefied  already. 

(6.)  Recent  experiments  with  electric  discharges  in  high  vacuums 
(Exp.  71,  p.  250),  have  yielded  remarkable  results  wliich  are  held,  by 
some,  to  show  the  existence  of  a  fourth  condition  of  matter.  For 
matter  in  this  "  ultra-gaseous "  state,  the  name  "  Radiant  Matter" 
has  been  proposed. 

6O.  What  is  a  Fluid  ? — A  fluid  is  a  body  whose 
molecules  easily  change  their  relative  positions. 

The  term  comprehends  liquids,  gases,  and  vapors. 

(a.)  In  a  liquid,  cohesion  is  more  powerful  than  repulsion  ;  in  an 
aeriform  body,  repulsion  is  the  more  powerful.  The  change  from 
the  liquid  to  the  aeriform  condition  is  caused  by  an  increase  of  the 
velocity  of  the  constituent  molecules,  such  increase  of  velocity  being 
a  thermal  effect. 


61.  Optional  Definitions.— (1.)  A  body  possessing  any 
degree  of  elasticity  of  form  (§  45)  is  a  solid  ;  a  body  that  possesses 
no  elasticity  of  form  is  a  fluid. 

(2.)  A  body  that  can  exist  in  equilibrium  under  the  action  of  a 
pressure  that  is  not  uniform  in  all  directions  is  a  solid ;  a  body  that 
cannot  exist  in  equilibrium  under  such  conditions  is  a  fluid. 


24  THE  THREE  CONDITIONS  OF  MATTER. 

(3.)  A  fluid  that  can  expand  indefinitely  so  as  to  fill  any  vessel, 
however  large,  is  an  aeriform  body ;  a  fluid,  a  small  portion  of  which, 
when  placed  in  a  large  vessel,  does  not  expand  at  once  so  as  to  fill 
the  vessel,  but  remains  collected  at  the  bottom,  is  a  liquid. 

(4.)  A  body  that  has  a  definite  volume  and  form  is  a  solid  ;  a  body 
that  has  a  definite  volume  and  an  indefinite  form  is  a  liquid ;  a  body 
ihat  has  an  indefinite  volume  and  form  is  aeriform. 

(5.)  A  gas  is  an  easily  compressible  fluid. 

62.  Kinetic  Theory  of  Gases.— A  perfect  gas 
consists  of  free,  elastic  molecules  in  constant  motion. 
Each  molecule  moves  in  a  straight  line  and  with  a  uni- 
form velocity  until  it  strikes  another  molecule  or  the  ves- 
sel in  which  the  gas  is  contained.  The  blows  that  the 
molecules  thus  strike  upon  the  vessel  are  so  numerous 
that  their  total  effect  is  a  continuous,,  constant  force  or 
pressure. 

(a.)  The  mean  velocity  of  a  hydrogen  molecule  has  been  deter- 
mined as  184260  cm.  (or  more  than  a  mile)  per  second.  If  its 
weight  were  known,  the  work  that  it  can  do  might  be  easily  com- 
puted (§  157).  The  molecules  of  other  aeriform  substances  move 
with  smaller  velocities. 

Recapitulation. — To  be  reproduced,  upon  paper  or 
the  blackboard,  by  each  pupil. 


MATTER i 


SOLIDS. 

Molecules  change 
their  relative  po- 
sitions with  diffi- 
culty. 


FLUIDS. 

Molecules  change 
their  relative  po- 
sitions easily. 


LIQUIDS, 

Molecules  cling  to- 
gether feebly. 


AERIFORM  BODIES. 
Molecules    tend    to 
separate. 


GASES  ;  ordinarily 
aeriform. 

KINETIC  THEORY. 
VAPORS;  ordinarily 
liquid  or  solid. 


DYNAMICS.— FORCE  AND   MOTION.— GRAVITATION.— 

FALLING    BODIES.— THE    PENDULUM.— 

ENERGY. 


ECTION  I. 


FORCE    AND    MOTiO  N. 

63.  Dynamics. — Dynamics   is   that   branch  of 
physics  which  treats  of  forces  and  their  effects. 

These  effects  may  be  of  two  kinds. 

(a.)  The  forces  employed  may  be  counterbalanced.  If  they  thus 
act  upon  a  body  at  rest,  that  body  will  remain  at  rest ;  if  they  act 
upon  a  body  in  motion,  the  motion  will  not  be  changed  thereby. 
The  branch  of  dynamics  that  treats  of  forces  thus  balanced  is  called 
Static*. 

(6.)  The  forces  employed  may  act  against  the  inertia  of  matter 
(§  38),  and  produce  motion  or  change  of  motion.  The  branch  of 
dynamics  that  treats  of  forces  thus  used  is  called  Kinetics.  If  we 
have  a  problem  relating  to  the  forces  that  may  produce  equilibrium 
in  a  lever,  as  in  the  act  of  weighing  goods,  it  is  a  static  problem  ; 
if  a  problem  refer  to  the  velocity  of  a  falling  body,  or  the  amount 
of  work  that  may  be  done  by  the  uncoiling  of  a  watch-spring,  it  is 
a  kinetic  problem. 

Note. — No  attempt  will  be  made  to  maintain  the  distinction  be 
tween  the  static  and  kinetic  effects  of  forces. 

64.  What  is  Force  ?— The  word  force  is  difficult 
of  satisfactory  definition.     As  generally  used,  it  signifies 


26  FORCE  AND    MOTION. 

any  cause  that  tends  to  produce,  change  or  destroy 
motion. 

It  follows  from  inertia  that  bodies  are  incapable  of 
changing  their  condition  of  rest  or  motion.  Any  cause 
capable  of  producing  a  tendency  to  change  either  of  these 
conditions,  is  called  a  force.  Equal  forces  will  produce 
equal  velocities  when  applied  to  the  same  body  for  the 
same  time. 

(a.)  We  say  that  the  tendency  of  a  force  acting  on  a  body  at  rest 
fs  to  move  it.  Motion  loill  be  produced  if  the  body  is  free  to  move. 
This  motion  may  be  prevented  by  the  simultaneous  action  of  another 
force  or  of  other  forces.  Or  the  body  may  be  fixed  so  that  a  given 
pull  or  pressure,  {.  e.,  the  application  of  force,  will  produce  no 
motion.  In  this  case,  opposing  forces  are  called  into  action  as  soon 
as  the  given  force  begins  to  act,  and  thus  the  new  force  is  neutralized. 
For  instance,  a  small  boy  may  exert  all  of  his  muscular  power  upon 
a  large  stone  and  not  lift  it  at  all.  The  force  employed  produces  no 
motion.  The  attraction  between  the  earth  and  the  stone  (§  33)  is  a 
force  acting  in  a  downward  vertical  direction.  This  force  is  exactly 
balanced  by  the  upward  pressure  of  the  supporting  earth  or  floor 
(§  93).  If  the  stone  weighs  two  hundred  pounds  and  the  boy  lifts 
fifty  pounds,  the  supporting  body  exerts  an  upward  pressure  of  only 
one  hundred  and  fifty  pounds.  One  quarter  of  the  weight  of  the 
stone  or  a  downward  force  of  fifty  pounds  is  thus  liberated  or  called 
into  play  by  the  very  act  of  lifting  with  a  force  of  fifty  pounds. 
Hence  no  motion  is  produced,  because  an  opposing  force  is  called 
into  action  as  soon  as  the  given  force  begins  to  act,  and  thus  the 
new  force  is  neutralized. 

(&.)  In  this  case,  the  greatest  opposing  force  that  can  be  set  free 
or  called  into  play  is  a  force  of  two  hundred  pounds,  the  full  weight 
of  the  stone.  If,  therefore,  the  stone  be  lifted  with  a  force  of  more 
than  two  hundred  pounds,  the  new  force  can  not  be  wholly  neutralized 
and  motion  will  take  place.  If  the  body  be  free  to  move,  the  smallest 
conceivable  force  will  overcome  the  inertia  and  produce  motion. 

65.  Elements  of  a  Force. — In  treating  of  forces, 
we  have  to  consider  three  things : 
(1.)  The  point  of  applicationf  or  the  point  at  which 
the  force  acts. 


FOKCE  AND  MOTIOtf.  27 


(£.)  The  direction,  or  the  right  line  along  which  it 
tends  to  move  the  point  of  application. 

(3.)  The  magnitude  or  value  when  compared  with  a 
given  standard,  or  the  relative  rate  at  which  it  is 
able  to  produce  motion  in  a  hody  free  to  move. 

66.  Measurement  of  Forces.—  It  frequently  is 
desirable  to  compare  the  magnitudes  of  two  or  more  forces. 
That  they  may  be  compared,  they  must  be  measured  ;  that 
they  may  be  measured,  a  standard  of  measure  or  unit  of 
force  is  necessary.     When  this  unit  has  been  determined 
upon,  the  value  of  any  given  force  is  designated  by  a  nu- 
merical reference  to  the  unit,  just  as  we  refer  quantities  of 
weight  to  the  kilogram  or  pound,  or  quantities  of  distance 
to  the  meter  or  yard.     The  magnitude  of  any  force  may  be 
measured  by  either  of  two  units,  which  we  shall  now  con* 
sider. 

67.  The  Gravity  Unit.—  The  given  force  may  be 
measured  by  comparing  it  with  the  gravity  of  some  known 
quantity  or  mass  of  matter.    This  is  a  very  simple  and 
convenient  way,  and  often  answers  every  purpose,     ^e 
gravity  unit  of  force  is  the  gravity  of  any  unit  of 
mass.     This  unit  of  mass  may  be  a   gram,  kilogram, 
pound,  or  ton,  or  any  other  unit  that  may  be  more  con- 
venient under  the  circumstances.     (See  §  102.) 

(a.)  A  force  is  said  to  be  a  force  of  100  kilograms  when  it  may  be 
replaced  by  the  action  of  a  weight  of  100  kilograms.  The  pressure 
of  steam  in  a  boiler  is  generally  measured,  at  present,  in  pounds  p&r 
square  inch,  that  is,  by  determining  the  number  of  pounds  with 
which  it  would  be  necessary  to  load  down  a  movable  horizontal 
square  inch  at  the  top  of  the  boiler  in  order  to  keep  it  in  place 
against  the  pressure  of  the  steam.  A  cord  or  rope  may  be  pulled 
with  a  certain  force.  This  force  is  measured  by  finding  out 


£8  FORCE  AND  MOTTO W. 

many  pounds  suspended  by  the  cord  or  rope  would  give  it  an  equal 
pull  or  tension. 

(b.)  As  we  shall  see,  the  force  of  gravity  exerted  upon  a  given 
mass  is  variable.  A  given  piece  of  iron  would  weigh  more  at  the 
poles  than  at  the  equator.  Other  variations  in  the  force  of  gravity 
are  known  When,  therefore,  scientific  accuracy  is  required,  it  wili 
not  suffice  to  speak  of  a  force  of  ten  pounds,  but  we  may  speak  of  a 
force  of  ten  pounds  at  the  sea-level  at  New  York  City.  The  neces- 
sary corrections  may  then  be  made.  But  for  ordinary  purposes, 
&ese  details  may  be  disregarded. 

68.  The  Absolute   Unit.— The  absolute  or  ki- 
netic  unit  of  force   is  the  force  that,   acting    for 
unit  of  time  upon  unit  of  mass,  will  produce  unit 
9f  velocity. 

The  foot-pound-second  (F.  P.  S.)  unit  of  force  is  the 
force  that,  applied  to  one  pound  of  matter  for  one  second, 
will  produce  a  velocity  of  one  foot  per  second. 

(a.)  In  all  kinetic  questions  the  kinetic  unit  is  far  more  convenient. 
Gravity  units  may  easily  be  changed  to  kinetic  units.  At  the  lati- 
tude of  New  York,  the  force  of  gravity  acting  upon  one  pound  of 
matter  left  free  to  fall  will  give  it  a  velocity  of  32.16  ft.  per  second 
for  every  second  that  it  acts.  Consequently,  at  such  latitudes,  the 
gravity  unit  is  equal  to  32.16  kinetic  units.. 

69.  The  Dyne.— Instead  of  using  a  unit  of  force 
based  upon  the  foot  and  pound,  scientific  men  are  coming 
to  use  a  similar  unit  based  upon  the  centimeter  and  gram. 
This  unit  has  a  definite  name.     The  dyne  is  the  force 
that,  acting   for  one   second  upon  a  mass  of  one 
gram,  produces  a  velocity  of  one  centimeter  per 
second. 

(a.)  If  a  body  weighing  25  grams  acquires  in  one  second  a  velocity 
of  30  cm.,  the  moving  force  was  750  dynes.  If  it  acquires  the  same 
velocity  in  2  seconds,  of  course  the  force  was  only  half  as  great,  or 
375  dynes.  As  the  increment  of  velocity  (§  127)  is  980  cm.,  the 
weight  of  a  gram  equals  980  dynes. 

(b.)  The  several  units  based  upon  the  centimeter,  gram  and  second, 


FORCE  AND  MOTION.  29 

constitute  a  class  called  (from  the  initial  letters  of  these  words) 
C.  G.  S.  Units.    Thus  the  dyne  is  the  C.  G.  S.  unit  of  force. 

Note  to  the  Pupil. — We  have  been  speaking  of  unit  of  mass,  and 
you  have  probably  had  no  difficulty  in  understanding  that,  by  this 
term,  a  certain  definite  quantity  of  matter  is  meant.  This  certain 
quantity  may  be  any  quantity  that  we  agree  upon  as  a  unit  of 
measure.  In  this  country  we  have,  as  yet,  no  commonly  accepted 
unit  of  mass.  In  countries  where  the  metric  system  of  weights 
and  measures  is  used,  the  unit  of  mass  is  the  quantity  of  matter 
contained  in  one  cu.  cm.  of  pure  water  at  its  temperature  of  greatest 
density.  It  will  be  seen  that  this  definition  is  independent  of  gravity, 
and  that  it  holds  good  for  matter  anywhere.  The  quantity  of  matter 
in  the  unit  thus  defined  is  invariable,  while  the  gram,  which  is  its 
weight  (§  36),  is  variable.  But  notwithstanding  this,  at  any  given 
place,  weight  is  proportional  to  mass,  and  we,  therefore,  conveniently 
use  weight  as  a  means  of  estimating  mass.  We  speak  t  without  any 
considerable  ambiguity  of  a  pound  of  matter,  because  we  know  that 
a  mass  that  weighs  two  pounds  at  the  same  place  has  just  twice  as 
much  matter  as  the  first,  which  we  may  take  as  a  convenient  unit  of 
mass. 

70.  Momentum. — The  momentum  of  cu  body  is 
Us  quantity  of  motion. 

Its  measure  is  the  product  of  the  numbers  representing 
the  mass  and  the  velocity. 

(a.)  One  tendency  of  force  is  to  produce  motion.  In  a  given 
time,  two  units  of  force  will  produce  twice  as  much  motion  as  one 
unit.  This  doubled  momentum  or  quantity  of  motion  may  exist  in 
two  units  of  mass  having  one  unit  of  velocity,  or  in  one  unit  of 
mass  with  two  units  of  velocity.  The  momentum  of  a  body  having 
a  mass  of  20  pounds  and  a  velocity  of  15  feet,  is  twice  as  great  as 
that  of  a  body  having  a  mass  of  5  pounds  and  a  velocity  of  30  ft. 
The  momentum  of  the  former  is  300 ;  that  of  the  latter,  150.  Mo- 
mentum has  reference  only  to  force  and  inertia.  Therefore,  when 
acting  upon  bodies  free  to  move,  equal  forces  will  produce  equal 
momenta  whether  the  bodies  acted  upon  be  light  or  heavy.  The 
unit  of  momentum  has  no  definite  name. 

71.  Experiment. — Figure   6   represents  a  piece  of 
apparatus,  devised  by  Ritchie  of  Boston.     It  consists  of 


30 


FORCE  AND  MOTION. 


two  ball  pendulums,  one  of  which  weighs  twice  as  much 

as  the  other,  suspended  as 
represented.  The  heavier  ball 
contains  a  spring-hammer, 
which  is  held  back  by  a  thread. 
The  hammer  being  thus  held 
back,  and  the  smaller  ball 
resting  against  its  face,  the 
thread  is,  burned,  a  blow  is 
struck,  and  an  equal  force  is 
exerted  upon  each  ball  (§§  72 
[3]  and  93).  The  smaller  ball 
will  move  twice  as  fast  and 
twice  as  far  as  the  larger  ball, 


FIG.  6. 


equal  forces  producing  equal  momenta. 
EXERCISES. 

1.  Find  the  momentum  of  a  500  Ib.  ball  moving  500  feet  a  second. 

2.  By  falling  a  certain  time,  a  200  Ib.  ball  has  acquired  a  velocity 
of  321.6  ft.     What  is  its  momentum? 

8.  A  boat,  that  is  moving  at  the  rate  of  5  miles  an  hour,  weighs 
4  tons ;  another,  that  is  moving  at  the  rate  of  10  miles  an  hour, 
weighs  2  tons.  How  do  their  momenta  compare  ? 

4.  What  is  meant  by  a  force  of  10  pounds  ?    To  how  many  F.  P.  S. 
units  is  it  equal  ? 

5.  A  stone  weighing  12  oz.  is  thrown  with  a  velocity  of  1820  ft. 
per  minute.     An  ounce  ball  is  shot  with  a  velocity  of  15  miles  per 
minute.    Find  the  ratio  between  their  momenta. 

6.  An  iceberg  of  50,000  tons  moves  with  a  velocity  of  2  miles  an 
hour  ;  an  avalanche  of  10,000  tons  of  snow  descends  with  a  velocity 
of  10  miles  an  hour.     Which  has  the  greater  momentum  ? 

7.  Two  bodies  weighing  respectively  25  and  40  pounds  have  equal 
momenta.     The  first  has  a  velocity  of  60  ft.  a  second  ;  what  is  thn 
velocity  of  the  other  ? 

$.  Two  balls  have  equal  momenta.     The  first  weighs  100  kilo 


FORCE  AND  MOTION.  31 

grams  and  moves  with  a  velocity  of  20  meters  a  second.  The  other 
moves  with  a  velocity  of  500  meters  a  second.  What  is  its  weight  \ 

9.  A  force  of  1000  dynes  acts  on  a  certain  mass  for  one  second  and 
gives  it  a  ve.^city  of  20  cm.  per  second.      What  is  the  mass  in 
grams?  Ans.  50. 

10.  A  constant  force,  acting  on  a  mass  of  12  g.  for  one  second       Q 
gives  it  a  velocity  of  6  cm.  per  second.     Find  the  force  in  dynes. 

11.  A  force  of  490  dynes  acts  on  a  mass  of  70  g.  for  one  second. 
What  velocity  will  be  produced  ?  Ans.  7  cm.  per  second. 

12.  Two  bodies  start  from  a  condition  of  rest  and  move  towarda       L  • 
each  other  under  the  influence  of  their  mutual  attraction  (§§  7  and 

98).  The  first  has  a  mass  of  1  g. ;  the  second,  a  mass  of  100  g.  The 
force  of  attraction  is  T^  dyne.  What  will  be  the  velocity  acquired 
by  each  during  one  second  ? 

72.  Laws  of  Motion. — The  following  propositions, 
known  as  Newton's  Laws  of  Motion,  are  so  important  and 

so  famous  in  the  history  of  physical  science  that  they       ^ 
ought  to  be  remembered  by  every  student : 

(1.)  Every  body  continues  in  its  state  of  rest  or 
of  uniform  motion  in  a  straight  line 
unless  compelled  to  change  that  state  by 
an  external  force. 

(2.)  Every  motion  or  change  of  motion  is  in  the 
direction  of  the  force  impressed  and  is 
proportionate  to  it. 

(3.)  Action  and  reaction  are  equal  and  opposite 
in  direction. 

73.  The  First  Law.— The  first  law  of  motion  re- 
sults directly  from  inertia   (§  38).    It  is  impossible  to 
furnish  perfect  examples  of  this  law  because  all  things 
within  our  reach  or  observation  are  acted  upon  by  some 
external  force.     A  base-ball  when  once  set  in  motion  has 
no  power  to  stop  itself  (§  38,  a).     If  it  moved  in  obe- 


32  FORCE  AND  MOTION. 

dience  to  the  muscular  impulse  only,  its  motion  would  be 
in  a  straight  line ;  but  the  force  of  gravity  is  ever  active, 
and  constantly  turns  it  from  that  line,  and  forces  it  to 
move  in  a  graceful  curve  instead. 

74.  Centrifugal  Force.— Although  it  is  obviously 
impossible  to  give  any  direct  experimental  proof  of  the  first 


FIG.  7. 

law  of  motion,  we  see  many  illustrations  of  the  tendency 
of  moving  bodies  to  move  in  straight  lines  even  when 
forced  to  move  in  curved  lines.  A  curved  line  may  be 
considered  a  series  of  infinitely  small  straight  lines.  A 
body  moving  in  a  curve  has,  by  virtue  of  its  inertia,  a 
tendency  to  follow  the  prolongation  of  the  small  straight 
line  in  which  it  chances  to  be  moving.  Such  a  prolonga- 
tion becomes  a  tangent  to  the  curve,  to  move  in  which  a 
body  must  fly  further  from  the  centre.  This  tendency 


FORCE  AND  MOTION. 

of  matter  to  move  in  a  straight  line,  and,  conse- 
quently, further  away  from  the  centre  around 
which  it  is  revolving,  is  called  Centrifugal  Force, 
from  the  Latin  words  which  mean  to  fly  from  the  centre. 
The  "laws"  of  this  "centrifugal  force"  may  be  studied 
or  illustrated  by  the  whirling-table  and  accompanying 
apparatus,  represented  in  Figure  7.  (See  §  77.) 

75.  Caution. — It  is  to  be  noticed  that  this  so-called 
"  Centrifugal  Force "  is  not  a  force  at  all.    It  is 
simply  inertia  manifested  under  special  conditions.    It  is 
one  of  the  universal  properties  of  matter  by  virtue  of 
which  the  body  shows  a  decided  determination  to  obey 
the  first  law  of  motion.    The  facts  of  the  case  are  the 
direct  opposite  of  those  implied  by  this  ill-chosen  name. 
Take  a  common  sling,  for  instance.   The  implication  made 
by  the  term,  "  Centrifugal  Force,"  is  that  the  pebble  in  the 
revolving  sling  has  a  natural  tendency  to  continue  moving 
in  a  circle,  and  that  some  external  force  is  necessary  to 
overcome  that  tendency.     The  truth  is  that  the  natural 
tendency  of  the  pebble  is  to  move  in  a  straight  line,  and  the 
only  reason  that  it  does  not  thus  move  is  that  it  is  continu- 
ally forced  from  its  natural  path  by  the  pull  of  the  string. 
As  soon  as  this  external  force  is  removed,  by  intent  or 
accident,  away  flies  the  stone  in  obedience  to  its  own  law- 
abiding  tendencies. 

76.  Simply  Suggestive.— Examples  and  effects  of 
this  so-called  centrifugal  force  may  be  suggested  as  follows: 
Wagon  turning  a  corner,  railway  curves,  water  flying  from 
a  revolving  grindstone,  broken  fly-wheels,  spheroidal  form 
of  the  earth,  erosion  of  river-beds,  a  pail  of  water  whirled 
in  a  vertical  circle,  the  inward  leaning  of  the  circus-horse 
%nd  rider,  the  centrifugal  drying  apparatus  of  the  laundry 


34  FORCE  AND   MOTION. 

or  sugar  refinery,  difference  between  polar  and  equatorial 
weights  of  a  given  mass,  etc. 

77.  Law  of  Centrifugal  Force.— The  force  neces- 
sary to  overcome  this  tendency  of  matter  to  move  away 
from  the  centre  around  which  it  may  be  revolving,  varies 
directly  as  the  mass  and  as  the  square  of  the  velocity,  the 
radius  remaining  the  same.    Doubling  the  mass  doubles 
the  force  needed,  but  doubling  the  velocity  quadruples  the 
needed  restraining  force. 

78.  The  Second  Law. — The  second  law  of  motion 
is  sometimes  given  as  follows:   A  given  force  will  pro- 
duce the  same  effect  whether  the  body  on  which  it 
acts  is  in  motion  or  at  rest ;  whether  it  is  acted  on 
"by  that  force  alone  or  by  others  at  the  same  time. 

(a. )  Many  attempts  have  been  made  to  show  that  these  are  only 
two  ways  of  stating  the  same  proposition  ;  most  of  them  are  more 
perplexing  than  profitable.  In  the  law  as  given  by  Newton  (§  72), 
the  word  motion  is  doubtless  used  in  the  sense  of  momentum.  If  the 
substitution  of  "  momentum  "  for  "  motion  "  makes  the  reconciliation 
any  easier,  no  objection  can  be  made  to  the  substitution. 

79.  Resultant   Motion. — Motion   produced   by 
the  joint  action  of  two  or  more  forces  is  called 
resultant  motion. 

The  point  of  application,  direction,  and  magnitude  of 
each  of  the  component  forces  being  given,  the  direction 
and  magnitude  of  the  resultant  force  are  found  by  a 
method  known  as  the  composition  of  forces. 

80.  Composition   of  Forces. — Under  composi- 
tion of  forces,  three  cases  may  arise  : 

(1.)  When  the  given  forces  act  in  the  same  direc- 
tion. The  resultant  is  then  the  sum  of  the  given 
forces.  Example  :  Bowing  a  boat  down  stream. 


FORCE  AND  MOTION.  35 

When  the  given  forces  act  in  opposite  di- 
rections. The  resultant  is  then  the  difference 
between  the  given  forces.  Motion  will  be  pro- 
duced in  the  direction  of  the  greater  force.  Ex- 
ample :  Eowing  a  boat  up  stream. 
(3.)  When  the  given  forces  act  at  an  angle.  The  re- 
sultant is  then  ascertained  by  the  parallelogram  of 
forces.  Example :  Rowing  a  boat  across  a  stream. 

81.  Graphic   Representation    of  Forces.— 

Forces  may  be  represented  by  linest  the  point  of 
application  determining  one  end  of  the  line,  the  direc- 
tion of  the  force  determining  the  direction  of  the  line, 
and  the  magnitude  of  the  force  determining  the  length 
of  the  line. 

(a.)  It  will  be  noticed  that  these  three  elements  of  a  force  (§  65) 
are  the  ones  that  precisely  define  a  line.  By  drawing  the  line  as 
above  indicated,  the  units  of  force  being  numerically  equal  to  the 
units  of  length,  we  have  a  complete  graphic  representation  of  the 
given  force.  The  unit  of  length  adopted  in  any  such  representation 

may  be  determined  by  convenience; 
but  the  scale  once  determined,  it 
must  be  adhered  to  throughout  the 
problem.  Thus  the  diagram  rep- 
resents two  forces  applied  to  the 
point  B.  These  forces  act  at  right 
angles  to  each  other.  The  arrow- 
heads indicate  that  the  forces  rep 


FIG.  8.  resented  act  from  B  toward  A  and 

C  respectively.      The   force    that 

acts  in  the  direction  BA  being  20  pounds  and  the  force  acting  in  the 
direction  BC  being  40  pounds,  the  line  BA  must  be  one-half  as 
long  as  BC.  The  scale  adopted  being  1  mm.  to  the  pound,  the 
smaller  force  will  be  represented  by  a  line*  2  cm.  long,  and  the  greater 
force  by  a  line  4  cm.  long. 

(6.)  The  graphic  determination  or  representation  of  the  resultant 
in  the  first  two  cases  under  the  "  Composition  of  Forces "  is  too 
simple  to  need  any  explanation. 


36  FORCE  AND  MOTION. 

82.  Parallelogram  of  Forces.— In  the  diagram, 
let  AB  and  AC  represent 

A 

two  forces  acting  upon  the 
point  A.  Draw  the  two 
lotted  lines  to  complete  the 
parallelogram.  From  A,  the 
point  of  application,  draw 
the  diagonal  AD.  This 
diagonal  will  be  a  complete  graphic  representa- 
tion of  the  resultant.  In  such  cases  the  two  given 
forces  are  called  components.  The  resultant  of  any  two 
components  may  always  be  determined  in  this  way.  If 
two  forces,  such  as  those  represented  in  the  diagram,  act 
simultaneously  upon  a  body  at  A,  that  body  will  move 
over  the  path  represented  by  AD,  and  come  to  rest  at  D. 

(a.)  Suppose  that  instead  of  acting  simultaneously,  these  forces 
act  successively.  If  AC  act  first  for  a  given  time,  it  would  move  the 
body  to  C.  If  then  the  other  force  act  for  an  equal  time  it  would 
move  it  to  the  right  a  distance  represented  by  AB  or  its  equal  CD, 
and  the  body  be  left  at  D  as  before.  If  the  force  represented  by  AB 
acted  first  and  the  force  represented  by  AC  then  acted  for  an  equal 
time,  the  body  would  evidently  be  left  at  D.  Thus  we  see  that  these 
two  forces  produce  the  same  effect  whether  they  act  simultaneously 
or  successively. 

83.  Experimental    Verification.— This   prin- 
ciple of  the  parallelogram  of  forces  may  be  verified  by 
the  apparatus  represented  in  Fig.  10.      ABCD  is  a  very 
light  wooden  frame,  jointed  so  as  to  allow  motion  at  its 
four  corners.    The  lengths  of  opposite  sides  are  equal ;  the 
lengths  of  adjacent  sides  are  in  the  ratio  of  two  to  three. 
From  the  corners  B  and  0,  light,  flexible  silk  cords  pasa 
over  the  pulleys  M  and  N,  and  carry  weights,  W  and  w, 
of  90  and  60  ounces  respectively,  the  ratio  between  the 


FORCE  AND  MOTION. 


FIG.  10. 

weights  being  the  same  as  the  ratio  between  the  corres- 
ponding adjacent  sides  of  the  wooden  parallelogram.  A 
weight  of  120  ounces  is  hting  from  the  corner  A.  When 
the  wooden  frame  comes  to  rest  it  will  be  found  that  the 
sides  AB  and  AC  lie  in  the  direction  of  the  cords  which 
form  their  prolongations.  These  sides  AB  and  AC  are 
accurate  graphic  representations  of  the  two  forces  acting 
upon  the  point  A.  It  will  be  further  found  that  the 
diagonal  AD  is  vertical  and  twice  as  long  as  the  side  AC. 
Since  the  side  AC  represents  a  force  of  60  ounces,  AD  will 
represent  a  force  of  twice  60  ounces  or  120  ounces.  We 
thus  see  that  AD  fairly  represents  the  resultant  of  the 
two  forces  due  to  the  gravity  of  W  and  wf  for  this  result- 


38  FORCE  AND  MOTION. 

ant  is  equal,  and  opposite  to  the  vertical  force  which  is 
due  to  the  gravity  of  V,  and  this  balances  the  forces  repre- 
sented by  AB  and  AC.  Results  equally  satisfactory  will 
be  secured  as  long  as  AB  :  AC  ::  W  :  w. 

84.  A   Substitute. — Very  satisfactory  results  may 
be  had  by  simpler  apparatus.     Let  H 

and  K  represent  two  pulleys  that  work 
with  very  little  friction.  Fix  them  to  a 
vertical  board.  The  blackboard  will 
answer  well  if  the  pulleys  can  be  at- 
tached without  injury.  Three  silk  cords 
are  knotted  together  at  0  ;  two  of  them 
pass  over  the  pulleys;  the  three  cords 
carry  weights,  P,  Q,  and  R,  as  shown  in  FIG.  n. 

the  figure.  R  must  be  less  than  the 
sum  of  P  and  Q.  When  the  apparatus  has  come  to  rest, 
take  the  points  A  and  B  so  that  AO  :  BO  : :  P  :  Q.  Com- 
plete the  parallelogram  AOBD  by  drawing  lines  upon  the 
vertical  board.  Draw  the  diagonal  OD.  It  will  be  found 
by  measurement  that  AO  :  OD  : :  P  :  R;  or  that  BO  :  OD 
: :  Q  :  R.  Either  equality  of  ratios  affords  the  verification 
sought. 

85.  Determination   of   the   Value   of   the 
Resultant. — With  a  carefully-constructed  diagram  (only 
half  of  the  parallelogram  need  be  actually  drawn)  the  re- 
sultant may  be  directly  measured  and  its  value  ascertained 
from  the  scale  adopted.    The  value  and  direction  of  the 
resultant  may  be  found  trigonometrically,  without  actual 
construction  of  the  diagram,  when  the  angle  between  the 
directions  of  the  components  is  known.     In  one  or  two 
cases,  however,  the  mathematical  solution  is  easy  without 


FORCE  AND  MOTION.  39 

the  aid  of  trigonometrical  formulae.  When  the  com- 
ponents act  at  right  angles  to  each  other,  the  resultant  is 
the  hypothenuse  of  a  right-angled  triangle.  (See  Olney^s 
Geometry,  paragraph  346.)  When  the  components  are 
equal  and  include  an  angle  of  120°,  the  resultant  divides 
the  parallelogram  into  two  equilateral  triangles.  It  is 
equal  to  either  component,  and  makes  with  either  an  angle 
of  60°.  (Let  the  pupil  draw  such  a  diagram.) 

86.  Equilibrant.— A  force   whose   effect   is   to 
balance  the    effects  of  the    several    components  is 
called  an  equilibrant.    It  is  numerically  equal  to  the 
resultant,  and  opposite  in  direction.     Thus  in  Fig.  10,  the 
gravity  of  the  weight  V  is  the  equilibrant  of  W  and  w ; 
it  is  equal  and  opposite  to  the  resultant  represented  by 
AD. 

87.  Triangle  of  Forces. — By  reference  to  Fig.  9, 
it  will  be  seen  that  if  AC  represent  the  magnitude  and 
direction  of  one  component,  and  CD  the  magnitude  and 
direction  of  the  other  component,  the  line  AD,  which 
completes  the  triangle,  will  represent  the  direction  and 
intensity  of  the  resultant.     Where  the  point  of  application 
need  not  be  represented,  this  method  of  finding  the  rela- 
tive magnitudes  and  directions  is  more  expeditious  than 
the  one  previously  given.    If  the  line  which  completes  the 
triangle  be  measured  from  D  to  A,  that  is  to  say,  in  the 
order  in  which  the  components  were  taken,  it  represents 
the  equilibrant ;   the  arrow-head  upon  AD  should  then 
be  turned  the  other  way.     If  this  line  be  measured  from 
A  to  D,  that  is,  in  the  reverse  order,  it  represents  the 
resultant* 


40 


FORCE  AND  MOTION. 


88.  Composition  of  More  than  Two 
-Forces. — If  more  than  two  forces  act  upon  the  point  of 
application,  the  resultant  of  any  two  may  be  combined 
with  a  third,  their  resultant  with  a  fourth,  and  so  on. 
The  last  diagonal  will  represent  the  resultant  of  all  the 
given  forces.  Suppose  that  four 
forces  act  upon  the  point  A,  as 
represented  in  the  diagram.  By 
compounding  the  two  forces  AB 
and  AC,  we  get  the  partial  re- 
sultant, A/*;  by  compounding 
this  with  AD,  we  get  the  second 
partial  resultant,  Ar';  by  com- 
pounding  this  with  AE,  we  get 
the  resultant,  AE. 


FIG.  12, 


89.  Polygon  of  Forces. — This  resultant  may  be 
more  easily  obtained  by  the  polygon  of  forces.  If  a  num- 
ber of  forces  be  in  equilibrium, 
they  may  be  graphically  repre- 
sented by  the  sides  of  a  closed 
polygon  taken  in  order.  If  the 
forces  are  not  in  equilibrium,  the 
lines  representing  them  in  magni- 
tude  and  direction  will  form  a 
figure  which  does  not  close.  The  line  that  completes  the 
figure  and  closes  the  polygon  will,  when  taken  in  the  same 
order,  indicated  by  the  arrow-head  at  x,  represent  the 
equilibrant ;  when  taken  in  the  opposite  order,  indicated 
by  the  arrow-head  at  z,  it  will  represent  the  resultant. 
This  will  be  evident  from  a  comparison  of  the  diagram  with 
the  one  preceding,  the  forces  compounded  being  the  same, 


FIG.  13. 


FORCE  AND   MOTION.  41 

90.  Parallelepiped  of  Forces. — The  component 

forces  may  not  all  act  in   the 
same  plane,  but  the  method  of 
composition  is   still  the  same. 
\      In  the  particular  case  of  three 
such  forces  it  will  be  readily 
seen  that  the  resultant  of  the 
FlG  forces  AB,  AC,  and  AD  is  rep- 

resented  by  AR,  the  diagonal 

of  the  parallelepiped  constructed  upon  the  lines  represent- 
ing these  forces. 

91.  Resolution  of  Forces. — The   operation  of 
finding  the  components  to  which  a  given  force  is 
equivalent  is  called  the  resolution  of  forces. 

It  is  the  converse  of  the  composition  of  forces.  Repre- 
sent the  given  force  by  a  line.  On  this  line  as  a  diagonal 
construct  a  parallelogram.  An  infinite  number  of  such 
parallelograms  may  be  constructed  with  a  given  diagonal. 
When  the  problem  is  to  resolve  or  decompose  the  given 
force  into  two  or  more  components  having  given  directions, 
it  is  definite — only  one  construction  being  possible.  The 
sides  that  meet  at  the  point  of  application  will  represent 
the  component  forces.  (See  §  201.) 

92.  Example  of  Resolution  of  Forces. — As 

we  proceed  we  shall  find  more  than  one  example  of  the 
resolution  of  forces.  A  single  one  will  answer  in  this 
place.  It  is  a  familiar  fact  that  a  sail-boat  may  move  in  a 
direction  widely  different  from  that  of  the  propelling  wind, 
and  that,  under  such  circumstances,  the  velocity  of  the 
boat  is  less  than  it  would  be  if  it  were  sailing  in  the  direc- 
tion of  the  wind,.  The  force  due  to  the  pressure  of  the 


4:2  FORCE  AND  MOTION. 

wind  is  twice  resolved,  and  only  one  of  the  components 
is  of   use  in   urging  the  boat  forward.    In  Figure  15, 
let  KL  represent  the  keel  of  the 
boat ;   BG,  the  position  of  the  sail ; 
andAB,  the  direction  and  intensity 
of  the  wind.      In  the  first  place, 
when  the  wind  strikes  the  sail  thus 
placed,  it  is  resolved  into  two  com- 
ponents— BG  parallel  to  the  sail,  and 
FIG.  15.  BD  perpendicular  to  the  sail.     It  is 

evident  that  the  first  of  tlhese  is  of 
no  effect.  But  the  boat  does  not  move  in  the  direction  of 
BD,  which  is,  in  turn,  resolved  by  the  action  of  the  keel 
and  rudder  into  two  forces,  BL  in  the  direction  of  the 
keel,  and  BE  perpendicular  to  it.  The  first  of  these  pro- 
duces the  forward  movement  of  the  boat ;  the  second 
produces  a  lateral  pressure  or  tendency  to  drift,  which  is 
more  or  less  resisted  by  the  build  of  the  boat 

93.  The  Third  Law.— Examples  of  the  third  law 
of  motion  are  very  common.    When  we  strike  an  egg 
upon  a  table,  the  reaction  of  the  table  breaks  the  egg ;  the 
action  of  the  egg  may  make  a  dent  in  the  table.    The  re- 
action of  the  air,  when  struck  by  the  wings  of  a  bird, 
supports  the  bird  if  the  action  be  greater  than  the  weight. 
The  oarsman  urges  the  water  backward  with  the  same 
force  that  he  urges  his  boat  forward.     In  springing  from 
a  boat  to  the  shore,  muscular  action  tends  to  drive  the 
boat  adrift ;  the  reaction,  to  put  the  passenger  ashore. 

94.  Reaction    in    Non-elastic  Bodies.— The 

effects  of  action  and  reaction  are   modified  largely  by 
elasticity,  but  never  so  as  to  destroy  their  equality.    Hang 


FORVE  AND  MOTION. 


43 


two  clay  balls  of  equal  mass  by  strings  of  equal  lengths 

BO  that  they  will  just  touch  each  other.     If  one  be  drawn 

aside  and  let  fall  against 

the  other,  both  will  move 

forward,  but  only  half  as 

far  as  the  first  would  had 

it  met  no  resistance.    The 

gain  of  momentum  by  the 

second  is  due  to  the  action 

of  the  first      It  is  equal 

to  the  loss  of  momentum 

6y  the  first,  which  loss  is 

due  to  the  reaction  of  the 

second. 

95.    Reaction     in 
Elastic    Bodies.  — If 

two  ivory  balls,  which  are 
elastic,  be  similarly  placed, 
and    the    experiment    re- 
peated, it  will  be  found  FIG.  16. 
that  the  first  ball  will  give 

the  whole  of  its  motion  to  the  second  and  remain  still 
after  striking,  while  the  second  will  swing  as  far  as  the 
first  would  have  done  if  it  had  met  no  resistance.  In  this 
case,  as  in  the  former,  it  will  be  seen  that  the  first  ball 
loses  just  as  much  momentum  as  the  second  gains. 

96.  Reflected  Motion.— Reflected  motion  u 
the  motion  produced  ~by  the  reaction  of  a  surface 
when  struck  by  a  body,  either  the  surface,  or  the 
body,  or  both  being  elastic. 

A  ball  rebounding  from  the  wall  of  a  house,  or  froni  thf 


44  FORCE  AND  MOTION. 

cushion  of  a  billiard-table,   is  an  example  of  reflected 
motion. 

97.  Law  -of  Reflected  Motion.— The  angle  in- 
cluded between  the  direction  of  the  moving  body  before  it 
strikes  the  reflecting  surface  and  a  perpendicular  to  thai 
surface  drawn  from  the  point  of  contact,  is  called  the  angle 


FIG.  17. 

of  incidence.  The  angle  between  the  direction  of  the 
moving  body  after  striking  and  the  perpendicular,  is  called 
the  angle  of  reflection.  TJie  angle  of  incidence  is 
equal  to  the  angle  of  reflection,  and  lies  in  the 
same  plane.  A  ball  shot  from  A  will  be  reflected  at  B 
back  to  C,  making  the  angles  ABD  and  CBD  equal. 

EXERCISES.     (Answers  to  le  written.) 

»  t.  Represent  graphically  the  resultant  of  two  forces,  100  and  150 
pounds  respectively,  exerted  by  two  men  pulling  a  weight  in  the 
same  direction.  Determine  its  value. 

J  2.  In  similar  manner,  represent  the  resultant  of  the  same  forces 
when  the  men  pull  in  opposite  directions.  Determine  its  value. 

3.  Suppose  an  attempt  be  made  to  row  a  boat  at  the  rate  of  foul 
miles  an  hour  directly  across  a  stream  flowing  at  the  rate  of  thre« 
miles  an  hour.     Determine  the  direction  and  velocity  of  the  boat. 

4.  A  flag  is  drawn  downward  64  ft.  from  the  mast-head  of  a  mov- 
ing ship.     During  the  same  time,  the  ship  moved  forward  24  ft. 
Represent  the  direction  and  length  of  the  actual  path  of  the  flag. 

5.  A  sailor  climbs  a  mast  at  the  rate  of  3  ft.  a  second  ;  the  ship  is 


FORCE  AND  MOTION. 


45 


sailing  at  the  rate  of  12  ft.  a  second.    Over  what  space  does  he 
actually  move  during  20  seconds  ? 

6.  A  foot-ball  simultaneously  receives  three  horizontal  blows  ;  one 
from  the  north  having  a  force  of  10  pounds;  one  from  the  east  having 
a  force  of-  15  pounds,  and  one  from  the  south-east  having  a  force 
of  804  kinetic  units.     Determine  the  direction  of  its  motion. 

7.  Why  does  a  cannon  recoil  or  a  shot-gun  "  kick  "  when  fired  ? 
Why  does  not  the  velocity  of  the  gun  equal  the  velocity  of  the  shot? 

8.  If  tine  river  mentioned  in  the  third  problem  be  one  mile  wide, 
how  far  did  the  boat  move,  and  how  much  longer  did  it  take  to  cross 
than  if  the  water  had  been  still  ? 

9.  A  plank  12  feet  long  has  one  end  on  the  floor  and  the  other  end 
raised  6  feet.    A  50-  pound  cask  is  being  rolled  up  the  plank.    Resolve 
the  gravity  of  the  cask  into  two  components,  one  perpendicular  to 
the  plank  to  indicate  the  plank's  upward  pressure,  and  one  parallel 
to  the  plank  to  indicate  the  muscular  force  needed  to  hold  the  cask 
in  place.    Find  the  magnitude  of  this  needed  muscular  force. 

10.  To  how  many  F.  P.  S.  units  of  force  is  the  weight  of  60  Ib. 
equal  ? 

11.  To  how  many  C.  GK  S.  units  of  force  is  the  weight  of  60  Kg. 
equal  ? 


o 


Recapitulation.  —  To  be  amplified  by  the  pupil  for 


revew. 


FORCE. 


STATICS. 
KINETICS* 

MOTION. 


ELEMENTS. 
MEASUREMENTS. 

"  CENTIFUGAL." 


GRAVITY  UNIT. 
KINETIC  UNIT.   Dyne. 


Components. 
Resultant. 


(  COMPOSITION.  \  ^uilibrant. 

Parallelogram 


GRAPHIC 

REPRESENTATION.     1  I   r  .          ° 

[RESOLUTION.        ^W^f*' 
(.  Polygon. 


MOMENTUM. 
NEWTON'S  LAWS. 
RESULTANT  MOTION. 
ACTION  AND  REACTION. 
REFLECTED  MOTION. 


46  QRAVTTATIOK 


XgJECTfON  H, 

J\. 

GRAVITATION. 

98,  What  is  Gravitation? — Every  particle  of 
matter  in    the   universe    has   an    attraction  for 
every    other   particle.      This    attractive   force    is 
called  gravitation. 

99.  Three   Important   Facts.— In   respect   to 
gravitation,  three  important  facts  have  been  established  : 

(1.)  It  acts  instantaneously.  Light  and  electricity 
require  time  to  traverse  space ;  not  so  with  this 
force.  If  a  new  star  were  created  in  distant 
space,  its  light  might  not  reach  the  earth  for 
hundreds  or  thousands  of  years.  It  might  be  in- 
visible for  many  generations  to  come,  but  its  pull 
would  be  felt  by  the  earth  in  less  than  the  twink- 
ling of  an  eye. 

(2.)  It  is  unaffected  "by  the  interposition  of  any 
substance.  During  an  eclipse  of  the  sun,  the 
moon  is  between  the  sun  and  the  earth.  But 
at  such  a  time,  the  sun  and  earth  attract  each 
other  with  the  same  force  that  they  do  at  other 
times. 

(3.)  It  is  independent  of  the  kind  of  matter,  but 
depends  upon  the  quantity  or  -mass  and 
the  distance.  "We  must  not  fall  into  the  error 
of  supposing  that  mass  means  size.  The  planet 
Jupiter  is  about  1300  times  as  large  as  the  earth, 
but  it  has  only  about  300  times  as  much  matter 
because  it  is  only  0.23  as  dense. 


GRAVITATION.  4? 

100.  Laws  of  Gravitation. — (1.)  Gravitation 
varies  directly  as  the  product  of  the  masses. 

(2.)  Gravitation  varies  inversely  as  the  square  of 
the  distance  (between  the  centres  of  gravity,  §  107). 

For  example,  doubling  the  product  doubles  the  attrac- 
tion ;  doubling  the  distance,  quarters  the '  attraction ; 
doubling  both  the  product  and  the  distance  will  halve  the 
attraction.  Trebling  the  product  will  multiply  the  attrac- 
tion by  three ;  trebling  the  distance  will  divide  the  attrac- 
tion by  nine  ;  trebling  both  the  product  and  the  distance 

will  divide  the  attraction  by  three  (  03  —  Q  )• 

101.  Equality    of    Attraction.  —  The    force 
exerted  by  one  body  upon  a  second  is  the  same  as 
that  exerted  by  the  second  upon  the  first. 

The  earth  draws  the  falling  apple  with  a  force  that  gives 
it  a  certain  momentum ;  the  apple  draws  the  earth  with  an 
equal  force  which  gives  to  it  an  equal  momentum. 

102.  Gravity. — The  most  familiar  illustration  of  grav- 
itation is  the  attraction  between  the  earth  and  bodies 
upon  or  near  its  surface.     This  particular  form  of  grav- 
itation is  commonly  called  gravity;  its  measure  is  weight; 
its  direction  is  that  of  the  plumb-line,  i.  e.,  vertical. 

103.  Weight. — The  weight  ofabody  varies  directly 
as  the  mass  and  inversely  as  the  square  of  the  distance 
between  its  centre  of  gravity  and  that  of  the  earth. 
The  mass  of  the  earth  remaining  constant,  doubling  the 
mass  of  the  body  weighed  doubles  the  product  of  the  masses 
(§  100)  and,  consequently,  doubles  the  weight.     When  we 
ascend  from  the  surface  there  is  nothing  to  interfere  with  the 
working  of  this  law ;  but  when  we  descend  from  the  surface 


48  OR  A  V1TATION. 

we  leave  behind  us  particles  of  matter  whose  attraction 
partly  counterbalances  that  of  the  rest  of  the  earth. 

104.  An    Example.— Consider  the  earth's  radius 
to  be  4,000  miles,  and  the  earth's  density  to  be  uniform. 
At  the  centre,  a  body,  whose  weight  at  the  surface  is 
100    pounds,    would    be    attracted    in    every    direction 
with  equal  force.     The  resultant  of  these  equal  and  oppo- 
site forces  would  be  zero,  and  the  body  would  have  no 
weight.     At  1,000  miles  from  the  centre,  one  fourth  of  the 
distance  to  the  surface,  it  would  weigh  25  pounds,  one- 
fourth  the  surface  weight ;  at  2,000  miles  from  the  centre, 
50  pounds ;  at  3,000  miles  from  the  centre,  75  pounds ;  at 
4,000  miles  from  the  centre,  or  the  surface  distance,  it 
would  weigh  100  pounds  or  the  full  surface  weight.    If 
carried  up  still  further,  the  weight  will  decrease  according 
to  the  square  of  the  distance.    At  an  elevation  of  4,000 
miles  above  the  surface  (8,000  miles  from  the  centre)  it 
will  weigh  25  pounds,  or  one-fourth  the  surface  weight. 

105.  Law  of  Weight. — Bodies  weigh  most  at 
the  surface  of  the  eaHh.     Below  the  surface,  the 
weight  decreases  as  the  distance  to  the  centre  de- 
creases.   Above  the  surface,  the  weight  decreases  as 
the  square   of  the   distance   from    the    centre  in- 
creases. 

106.  Formulas    for    Gravity   Problems.— 

Representing  the  surface  weight  by  W  and  the  surface  dis- 
tance (4,000  miles)  by  D,  the  other  weight  by  w,  and  the 
other  distance  from  the  earth's  centre  by  d,  the  above  la^v 
may  be  algebraically  expressed  as  follows: 

Below  the  earth's  surface :    w  :  W  : :  d  :  D. 

Above  the  earth's  surface :    w  :  W  : :  D2 :  d*. 


&  RA  VITA  T1ON.  49 


EXERCISES. 

1.  How  far  below  the  surface  of  the  earth  will  a  ten-pound  ball 
weigh  only  four  pounds? 

Solution. 

Formula  :  w  :  W::  d  :  D.      \  d=  1600,  the  number  of  miles 

Substituting  :       4  :  10  ::  d  :  4000  I  from  the  centre. 

4000  —  1600  —  2400,  the  number  of  miles  below  the  surface.— Am. 

2.  What  would  a  body  weighing  550  Ibs.  on  the  surface  of  the 
earth  weigh  3,000  miles  below  the  surface  ?  Ans.  137^  Ibs. 

3.  Two  bodies  attract  each  other  with  a  certain  force  when  they 
are  75  m.  apart.     How  many  times  will  the  attraction  be  increased 
when  they  are  50  m.  apart  ?  Ans.  2}-. 

4.  Given  three  balls.     The  first  weighs  6  Ibs.  and  is  25  ft.  distant 
from  the  third.     The  second  weighs  9  Ibs.  and  is  50  ft.  distant  from 
the  third,    (a)   Which  exerts  the  greater  force  upon  the  third? 
(&)    How  many  times  as  great  ?  Ans.  |. 

5.  A  body  at  the  earth's  surface  weighs  900  pounds  ;  what  would 
it  weigh  8,000  miles  above  the  surface  ? 

6.  How  far  above  the  surface  of  the  earth  will  a  pound  avoirdupois 
weigh  only  an  ounce?  Ans.  12,000  miles.    /  fc,o <0 

,  7.  At  a  height  of  3,000  miles  above  the  surface  of  the  earth, 
what  would  be  the  difference  in  the  weights  of  a  man  weighing  200 
Ibs.  and  of  a  boy  weighing  100  Ibs.  ?  Ans.  32.65  Ib. 

8.  Find  the  weight  of  a  180  Ib.  ball  (a)  2,000  miles  above  the 
earth's  surface  ;  (&)  2,000  miles  below  the  surface.^^-^-.    J0  fib* , 

9.  (a)   Would  a  50  Ib.  cannon  ball  weigh  more  1,000  miles  above 
the  earth's  surface,  or  1,000  miles  below  it  ?    (6)   How  much  ? 

10.  If  the  moon  were  moved  to  three  times  its  present  distance 
from  the  earth,  what  would  be  the  effect  (a)  on  its  attraction  for 
the  earth  ?    (&)   On  the  earth's  attraction  for  it  ? 

11.  How  far  below  the  surface  of  the  earth  must  an  avoirdupois 
pound  weight  be  placed  in  order  to  weigh  one  ounce  ?  <3  «-7<  o  -•* 

12.  How  far  above  the  surface  of  the  earth  must  2,700  pounds  be 
placed  to  weigh  1,200  pounds  ?  Ans.  2,000  miles. 

18.  What  effect  would  it  have  on  the  weight  of  a  body  to  double 
the  mass  of  the  body  and  also  to  double  the  mass  of  the  earth  V  ^ 

1O7.  Centre  of  Gravity.— The  centre  of  grav- 
ity of  a  body  is  the  point  about  which  all  the 
matter  composing  the  body  may  be  balanced. 

a 


50 


GRAVITATION. 


FlG.    18. 


The  force  of  gravity  tends  to  draw  every  particle  of 
matter  toward  the  centre  of  the  earth,  or  downward  in  a 

vertical  line.  We  may  therefore 
consider  the  effect  of  this  force 
upon  any  body  as  the  sum  of  an 
almost  infinite  number  of  paral- 
lel forces,  each  of  which  is  acting 
upon  one  of  the  molecules  of 
which  that  body  is  composed. 
We  may  also  consider  this  sum 
of  forces,  or  total  gravity,  as 
acting  upon  a  single  point,  just 
as  the  force  exerted  'by  two 
horses  harnessed  to  a  whiffle- 

tree  is  equivalent  to  another  force  (resultant)  equal  to  the 
sum  of  the  forces  exerted  by  the  horses,  and  applied  at  a 
single  point  at  or  near  the  middle  of  the  whiffle-tree. 
This  single  point,  which  may  thus  be  regarded  as  the 

point  of  application  of  the 
force  of  gravity  acting  upon  a 
body,  is  called  the  centre  of 
gravity  of  that  body.  In  other 
words,  the  weight  of  a  body 
may  be  considered  as  concen- 
trated at  the  centre  of  gravity. 

1O8.  How  to  find  the 
Centre  of  Gravity.  —  In 

a  freely  moving  body,  the  cen- 
tre of  gravity  will  be  broughi 
as  low  as  possible,  and  will, 
therefore,  lie  in  a  vertical  line 
FIG.  19.  drawn  through  the  point  of 


GRAVITATION.  5l 

support    This  fact  affords  a  ready  means  of  determining 
the  centre  of  gravity  experimentally. 

Let  any  irregularly  shaped  body,  as  a  stone  or  chair,  be 
suspended  so  as  to  move  freely.  Drop  a  plumb-line  from 
"he  point  of  suspension,  and  make  it  fast  or  mark  its  direc- 
tion. The  centre  of  gravity  will  lie  in  this  line.  From  a 
second  point,  not  in  the  line  already  determined,  suspend 
the  body ;  let  fall  a  plumb-line  as  before.  The  centre  of 
gravity  will  lie  in  this  line  also.  But  to  lie  in  both  lines,  the 
centre  of  gravity  must  lie  at  their  intersection.  (Fig.  19.) 

1O9.  May  be  Outside  of  the  Body.— The  cen- 
tre of  gravity  may  be  outside  of  the  matter  of  which  a 
body  consists,  as  in  the  case  of  a  ring,  hollow  sphere,  box, 
or  cask.  The  same  fact  is  illustrated  by  the  "  balancer," 
represented  in  the  figure.  The  centre 
of  gravity  is  in  the  line  joining  the 
two  heavy  balls,  and  thus  under  the 
foot  of  the  waltzing  figure.  But  the 
point  wherever  found  will  have  the 
same  properties  as  if  it  lay  in  the  mass 
of  the  body.  In  a  freely  falling  body, 
no  matter  how  irregular  its  form,  or 
how  indescribable  the  curves  made  by 
any  of  its  projecting  parts,  the  line  of 
direction  in  which  the  centre  of  grav- 
ity or  point  of  application  moves  will 
be  a  vertical  line  (§  65  [2]  ). 

FIG.  20.  11O.  Equilibrium.— -Inasmuch 

as  the  centre  of  gravity  is  the  point  at 
which  the  weight  of  a  body  is  concentrated,  when  the 
centre  of  gravity  is  supported,  the  whole  body  will 


rest  in  a  state  of  equilibrium.  The  centre  of  gravity 
will  be  supported  when  it  coincides  with  the  point  of  sup- 
port, or  is  in  the  same  vertical  line  with  it. 

111.  Stable  Equilibrium. —  A  body  supported 
In  such  a  way  that,  when  slightly  displaced  from 
its  position  of  equilibrium,  it  tends  to  return 
to  that  position,  is  said  to  be  in  stable  equili- 
brium. Such  a  displacement  raises  the  centre  of  grav- 
ity. Examples:  a  disc  supported  above  the  centre;  a 
semi-spherical  oil-can ;  a  right  cone  placed  upon  its 
base ;  a  pendulum  or  plumb-line.  The  cavalry-man 
represented  in  Fig.  21,  is  in  stable  equilibrium,  and 
may  rock  up  and  down, 
balanced  upon  his  horse's 
hind -feet,  because  the 
heavy  ball  brings  the  cen- 
tre of  gravity  of  the  com- 
bined mass  below  the 
points  of  support.  The 
"balancer"  (Fig.  20)  af- 
fords another  example  of 
stable  equilibrium. 


Unstable  Equi-  FlG 

librium. — A  body  sup- 
ported in  such  a  way  that,  when  slightly  displaced 
from  its  position  of  equilibrium,  it  tends  to  fall 
further  from  that  position,  is  said:  to  be  in  unstable 
equilibrium.  Such  a  displacement  lowers  the  centre  of 
gravity.  The  body  will  not  come  to  rest  until  the  centre 
of  gravity  has  reached  the  lowest  possible  point,  when  it 
will  be  in  stable  equilibrium.  Examples:  A  disc  sup- 


GRAVITATION. 


53 


M 


ported  below  its  centre  ;  a  right  cone  placed  on  its  apex; 
an  egg  standing  on  its  end ;  or  a  stick  balanced  upright 
upon  the  finger. 

113.  Neutral  Equilibrium. — A  "body  supported 
in   such   a    way   that,    when    displaced   from    its 
position  of  equilibriuin,  it  tends  neither  to  return 
to  its  former  position  nor  to  fall  further  from  it, 
is  said  to  be  in  neutral  or  indifferent  equilibrium. 
Such  a  displacement  neither  raises  nor  lowers  the  centre 
ol  gravity.    Examples:  A  disc  supported  at  its  centre ;   a 
sphere  resting  on  a  horizontal  surface  ;  a  right  cone  rest- 
ing on  its  side. 

(a.)  In  the  accompanying  figure  M,  N  and  0  represent  three  cones 

placed  respectively 
in  these  three  con- 
ditions of  equili- 
brium. The  letter 
g  shows  the  posi- 
tion of  the  centre 
of  gravity  in  each 
If  a  body  have 
two  or  more  points 
of  support  lying  in 

the  same  straight  line,  the  body  wilt  be  in  neutral,  stable  or  unstable 
equilibrium  according  as  the  centre  of  gravity  lies  in  this  line,  is 
directly  below  it  or  above  it. 

114.  Line  of  Direction. — A  vertical  line  drawn 
downward  f?iom  the  centre  of  gravity  is  called  the 
line  of  direction.    As  we  have  seen,  it  represents  the 
direction  in  which  the  centre  of  gravity  would  move  if 
the  body  were  unsupported.    It  may  be  considered  as  a 
line  connecting  the  centre  of  gravity  of  the  given  body 
and  the  centre  of  the  earth. 

115.  The   Base. —  The    side    on   ivhich    a   body 
rests  is  called  its  base.    If  the  body  be  supported  on 


GRAVITATION. 


legs,  as  a  chair,  the  base  is  the  polygon  formed  by  joining 
the  points  of  support. 

116.  Stability.— fl^ett  the  line  of  direction 
falls  within  the  base,  the  body  stands ;  when  with- 
out the  base,  the  body  falls. 

In  the  case  of  the  tower  represented  in  Fig.  23,  if  the 
upper  part  be  removed,  the  line  of  direction  will  be  as 
shown  by  the  left  hand  dotted  line.  It  falls  within  the 
base,  and  the  tower  stands.  When  the  upper  part  is  fast- 
ened to  the  tower,  the  line  of  direction  is  represented  by 
the  right  hand  dotted  line.  This  falls 
without  the  base,  and  the  tower  falls. 
The  stability  of  bodies  is  measured 
by  the  amount  of  work  necessary  to 
overturn  them.  This  depends  upon 
the  distance  that  it  is  necessary  to 
raise  the  centre  of  gravity  (equivalent 
to  raising  the  whole  body),  that  the 
line  of  direction  may  fall  without  the 
base.  When  the  body  rests  upon  a 
point,  as  does  the  sphere,  or  upon  a 
line,  as  does  the  cylinder,  a  very  slight 
force  is  sufficient  to  move  it,  no  elevation  of  the  centre  of 
gravity  being  necessary.  The  broader  the  base,  and  the 
lower  the  centre  of  gravity,  the  greater  the  stability. 

117.  Illustrations  of  Stability.— Let  the  figure 
represent  the  vertical  section  of  a  brick  placed  upon  its 
side,  its  position  of  greatest 
stability.     In  order  to  stand 
the  brick  upon  its  end,  g,  the 
centre  of  gravity,  must  pass 
over  the  edge,c.    That  is  to 


FIG.  23. 


a 

FIG.  34. 


GRAVITATION.  55 

Bay,  the  centre  of  gravity  must  be  raised  a  distance  equal 
to  the  difference  between  ga  and  gc,  or  the  distance  na 
But  to  lift  g  this  distance  is  the  same  as  to  lift  the  whole 
brick  vertically  a  distance  equal  to  nc.  Now  draw  similar 
figures  for  the  brick  when  placed  upon  its  edge  and  upon 
its  end.  In  each  case  make  gn  equal  to  ga,  and  see  that 
the  value  of  nc  decreases.  But  nc  represents  the  distance 
that  the  brick,  or  its  centre  of  gravity,  must  be  raised 
before  the  line  of  direction  can  fall  without  the  base,  and 
the  body  be  overturned.  To  lift  the  brick,  or  its  centre  of 
gravity,  a  small  distance  involves  less  work  than  to  lift  it 
a  greater  distance.  Therefore,  the  greater  the  value  of  nc, 
the  more  work  required  to  overturn  the  body,  or  the 
greater  its  stability.  But  this  greater  value  of  nc  evidently 
depends  upon  a  larger  base,  a  lower  position  for  the  centre 
of  gravity,  or  both. 


FIG.  25. 


(#.)  These  facts  explain  the  stability  of  leaning  towers  like  those 
of  Pisa  and  Bologna.  In  some  such  towers  the  centre  of  gravity 
is  lowered  by  using  heavy  materials  for  the  lower  part  and  light 
materials  for  the  upper  part  of  the  structure.  It  is  difficult  to  stand 
upon  one  foot  or  to  walk  upon  a  tight  rope  because  of  the  smallness 


56 


GRAVITATION. 


of  the  base.  A  porter  carrying  a  pack  is  obliged  to  lean  forward  ; 
a  man  carrying  a  load  in  one  hand  is  obliged  to  lean  away  from  the 
load,  to  keep  the  common  centre  of  gravity  of  man  and  load  over 
the  base  formed  by  joining  the  extremities  of  his  feet.  Why  does  a 
person  stand  less  firmly  when  his  feet  are  parallel  and  close  together 
than  when  they  are  more  gracefully  placed  ?  Why  can  a  child  walk 
more  easily  with  a  cane  than  without  ?  Why  will  a  book  placed  on 
i  desk-lid  stay  there  while  a  marble  would  roll  off  ?  Why  is  a  ton 
of  stone  on  a  wagon  less  likely  to  upset  than  a  ton  of  hay  similarly 
placed? 

EXERCISES. 

Explanatory  Note, — The  first  problem  in  the  table  below  may  be 
read  as  follows :  What  will  be  the  weight  of  a  body  which  weighs 
1200  pounds  at  the  surface  of  the  earth,  when  placed  2000  miles 
below  the  surface  ?  When  placed  4000  miles  above  the  surface  ? 
(Radius  of  earth=:4000  miles.)  All  of  the  measurements  are  from 
the  surface. 


NUMBER  OP 
PROBLEM. 

BELOW  SURFACE. 

AT  SURFACE. 

ABOVE  SURFACE. 

Pounds. 

Miles  from 
Surface. 

Pounds. 

Pounds. 

Miles  from 
Surface. 

1 

, 

2000 

1200 

, 

4000 

2 

300 

? 

1200 

533i 

9 

3 

? 

3000 

800 

? 

6000 

4 

? 

1000 

150 

? 

1000 

5 

100 

? 

400 

100 

? 

6 

250 

3000 

? 

? 

4000 

*X.  7 

? 

1600 

? 

32 

6000 

8 

12£ 

? 

100 

25 

! 

9 

? 

8250 

480 

? 

2000 

10 

90 

f 

450 

50 

? 

11 

160 

? 

256 

? 

12000 

12 

201.6 

2600 

v 

16 

? 

13 

256 

? 

? 

40.96 

16000 

14 

20250 

? 

324000 

9000 

? 

15 

? 

3200 

? 

1280 

9000 

FALLING   BODIES.  57 

Recapitulation. — In  this  sectiou  we  have  considered 
Gravitation ;  Facts  concerning  it ;  its  Law ; 
Gravity;  Weight;  Law  of  Weight ;  Centre 
of  Gravity;  Equilibrium  and  Stability  oi 

Bodies. 

y 


ECTJON  Hi, 


FALLI  NG    BODIES. 

118.  A  Constant  Force.— The  tendency  of  force 
is  generally  to  produce  motion.     Acting  on  a  given  mass 
for  a  given  time,  a  given  force   will  produce  a  certain 
velocity.    If  the  same  force  acts  on  the  same  mass  for 
twice  the  time  it  will  produce  a  double  velocity.     A  force 
which,    thus    continues    to  act  uniformly    upon    a 
body,  even  after   the  body  has  begun   to  move,  is 
called  a  constant  force.    The  velocity  thus  produced 
is  called  a  uniformly  accelerated  velocity.     If  a  constant 
force  gives  a  body  a  velocity  of  10  feet  in  one  second,  it 
will  give  a  velocity  of  20  feet  in  two  seconds,  of  30  feet  in 
three  seconds,  and  so  on.     The  force  of  gravity  is  a  con- 
stant force  and  the  velocity  it  imparts  to  the  falling  body 
is  a  uniformly  accelerated  velocity. 

119.  Velocities    of    Falling    Bodies.— If    a 

feather  and  a  cent  be  dropped  from  the  same  height,  the 
cent  will  reach  the  ground  first.  This  is  not  because  the 
cent  is  heavier,  but  because  the  feather  meets  with  more 
resistance  from  the  air.  If  this  resistance  can  be  removed, 
the  two  bodies  will  fall  ecjiial  distances  iu  ec^ual  times, 


58 


FALLING  BODIES. 


or  will  fall  with  the  same  velocity.  This  resistance  may 
be  avoided  by  trying  the  experi- 
ment in  a  glass  tube  from  which 
the  air  has  been  removed.  The  re- 
sistances may  be  nearly  equalized  by 
making  the  two  falling  bodies  of 
the  same  size  and  shape  but  of  dif- 
ferent weights.  Take  an  iron  and 
a  wooden  ball  of  the  same  size,  drop 
them  at  the  same  time  from  an 
upper  window,  and  notice  that  they 
will  strike  the  ground  at  sensibly 
the  same  time. 

12O.  Reason  of  this  Equal- 
ity.— The  cent  is  heavier  than  the 
feather  and  is  therefore  acted  upon 
by  a  greater  force.  The  iron  ball 
has  the  greater  weight,  which  shows 
that  it  is  acted  upon  by  a  greater 
force  than  the  wooden  ball.  But 
this  greater  force  has  to  move  a 
greater  mass,  has  to  do  more  work 
For  the  greater  force  to  do  the 
greater  work  requires  as  much  time  us  for  the 
lesser  force  to  do  the  lesser  work.  The  working  force 
and  the  work  to  be  done  increase  in  the  same  ratio.  A 
regiment  will  march  a  mile  in  no  less  time  than  a  single 
soldier  would  do  it ;  a  thousand  molecules  can  fall  no  fm> 
ther  in  a  second  than  a  single  molecule  can. 

121.  Galileo's  Device. — To  avoid  the  necessity 
for  great  heights,  and  the  interference  of  rapid  motion 
with  accurate  observations,  Galileo  used  an  inclined 


FIG.  26. 


than  the  lesser  force. 


FALLING   BODIES.  59 

plane>  consisting  of  a  long  ruler  having  a  grooved  edge, 
down  which  a  heavy  ball  was  made  to  roll.  In  this  way 
he  reduced  the  velocity,  and  diminished  the  interfering 
resistance  of  the  atmosphere  without  otherwise  changing 
the  nature  of  the  motion. 
Let  AB  represent  a  plane  so 
inclined  that  the  velocity  of 
a  body  rolling  from  B  toward  A 
A  will  be  readily  observable. 
Let  0  be  a  heavy  ball.  The 
gravity  of  the  ball  may  be 
represented  by  the  vertical 

line  CD.  But  CD  may  be  resolved  into  CF,  which  repre- 
sents a  force  acting  perpendicular  to  the  plane  and  pro- 
ducing pressure  upon  it  but  no  motion  at  all,  and  CE, 
which  represents  a  force  acting  parallel  to  the  plane,  the 
only  force  of  any  effect  in  producing  motion.  It  may  be 
shown  geometrically  that 

EC  :  CD  ::  BG  :  BA.     (Olnetfs  Geometry,  Art.  341.) 

By  reducing,  therefore,  the  inclination  of  the  plane  we 
may  reduce  the  magnitude  of  the  motion -producing  com- 
ponent of  the  force  of  gravity  and  thus  reduce  the  velocity. 
This  will  not  affect  the  laws  of  the  motion,  that  motion 
being  changed  only  in  amount, 
not  at  all  in  character.  |fl  \\\\ 

122.  Attwood's  Device. 

— For  the  purpose  of  lessening 
the  velocity  of  falling  bodies 
without  changing  the  character 
of  the  motion,  Mr.  Attwood 
devised  a  machine  which  has  FIG.  28. 


FALLING  BODIES. 


taken  his  name.  Att- 
wood's  machine  consists 
essentially  of  a  wheel 
R,  about  six  inches 
in  diameter,  over  the 
grooved  edge  of  which 
are  balanced  two  equal 
weights,  suspended  by 
a  long  silk  thread,  which 
is  both  light  and  strong. 
The  axle  of  this  wheel 
is  supported  upon  the 
circumferences  of  four 
friction  wheels,  r,  r,  r,  r, 
for  greater  delicacy  of 
motion.  As  the  thread 
is  so  light  that  its 
weight  may  be  disre- 
garded, it  is  evident 
that  the  weights  will  be 
in  equilibrium  whatever 
their  position 

This  apparatus  is  sup- 
ported upon  a  wooden 
pillar,  seven  or  eight  feet 
high.  The  silk  cord 
carrying  K,  one  of  the 
weights,  passes  in  front 
of  a  graduated  rod 
which  carries  a  movabk 
ring  B,  and  a  movable 
platform  A.  At  the  top 
of  the  pillar  is  a  plate  n, 


FALLING  BODIES.  61 

which  may  be  fastened  in  a  horizontal  position  for  the 
support  of  K  at  the  top  of  the  graduated  rod.  This  plate 
may  also  be  dropped  to  a  vertical  position,  thus  allowing  K, 
when  loaded,  to  fall.  A  clock,  with  a  pendulum  beating 
seconds,  serves  for  the  measurement  of  time,  and  the  drop 
ping  of  the  plate  at  the  top  of  the  pillar.  A  weight  ol 
rider,  m,  is  to  be  placed  upon  K,  and  give  it  a  downward 
motion.  Levelling  screws  are  provided  by  means  of  which 
the  graduated  rod  may  be  made  vertical,  and  K  be  made 
to  pass  through  the  middle  of  B. 

(a.)  Suppose  that  K  and  K'  weigh  315  grams  each,  and  that  the 
rider  m  weighs  10  grams.  When  m  is  placed  upon  K  and  the  plate 
dropped  by  the  action  of  the  clock,  the  gravity  of  m  causes  the 
weights  to  move.  We  now  have  the  motion  of  640  grams  produced 
by  the  gravity  of  only  10  grams.  When  this  force  (gravity)  moves 
only  10  grams  it  will  give  it  a  certain  velocity.  When  the  same 
fcrce  moves  640  grams  it  has  to  do  64  times  as  much  work,  and  can 
do  it  with  only  ¥\  the  velocity.  In  this  way  we  are  able  to  give  to 
K  and  m  any  velocity  of  fall  that  we  desire. 

123.  Experiments.— Arrange  the  apparatus  by  sup- 
porting K  and  m  upon  the  shelf  n.  As  the  hand  of  the 
clock  passes  a  certain  point  on  the  dial,  12  for  example, 
the  shelf  n  is  dropped  and  the  weights  begin  to  move.  By 
a  few  trials,  B  may  be  so  placed  that  at  the  end  of  one 
second  it  will  lift  m  from  K,  and  thus  show  how  far  the 
weights  fall  in  one  second.  Other  experiments  will  show 
how  many  such  spaces  they  will  fall  in  the  next  second  or 
in  two  seconds  ;  in  the  third  second  or  in  three  seconds ; 
in  the  fourth  second  or  in  four  seconds,  etc. 

Suppose  that  B  lifts  off  m  at  the  end  of  the  first  second. 
The  moving  force  being  no  longer  at  work,  inertia  will 
keep  K  moving  with  the  same  velocity  that  it  had  at  the 
end.  of  the  first  second.  By  placing  A  so  that  K  will  reach 
it  at  the  end  of  the  second  second,  the  distance  AB  wilJ 


62  FALLING  BODIES. 

indicate  the  velocity  with  which  K  was  moving  when  it 
passed  B  at  the  end  of  the  first  second.  In  a  similar  way 
the  velocity  at  the  end  of  the  second,  third,  or  fourth 
second  may  be  found. 

124.  Results. — Whatever  the  space  passed  over  in  the 
orst  second  by  the  weights  or  the  ball,  it  will  be  found 
that  there  is  an  uniform  increase  of  velocity.   Galileo  found 
that  if  the  plane  was  so  inclined  that  the  ball  would  roll 
one  foot  during  the  first  second,  it  would  roll  three  feet 
during  the  next  second,  five  feet  during  the  third,  and  so 
on,  the  common  difference  being  two  feet,  or  twice  the  dis- 
tance traversed  in  the  first  second. 

He  found  that  under  the  circumstances  supposed,  the 
ball  would  have  a  velocity  of  two  feet  at  the  end  of  the 
first  second,  of  four  feet  at  the  end  of  the  next,  of  six  feet 
at  the  end  of  the  third,  and  so  on,  the  increase  of  velocity 
during  the  first  second  being  the  same  as  the  increase 
during  any  subsequent  second. 

He  found  that,  under  the  circumstances  supposed,  the 
ball  would  pass  over  one  foot  during  one  second,  four  feet 
during  two  seconds,  and  nine  feet  during  three  seconds, 
and  so  on.  Similar  results  may  be  obtained  with  Att- 
wood's  machine. 

125.  Table  of  Results. — These  results  are  gener- 
alized in  the  following  table,  in  which  t  represents  any 
given  number  of  seconds : 


Number  of 
Seconds. 
I 

Spaces  fallen  during 
each  Second. 
1 

Velocities  at  the  End 
of  each  Second. 
2  

Total  Number  of 
Spaces  fallen, 
1 

2 

.    ..3  

4  

4 

3 

5  

6  

9 

4 

...7  

8.  

16 

etc. 
t  

etc. 

etc. 

m-^o.. 

etc.    * 

FALLING  BODIES.  63 

126.  Unimpeded    Fall.— By  transferring    matter 
from  K'  to  K,  the  velocity  with  which  the  weights  move 
will  be  increased.     When  all  of  K'  has  been  transferred  to 
K,  the  weights  will  fall,  in  this  latitude,  16.08  ft. 
or  4-9  ™-  during  the  first  second. 

If  the  plane  be  given  a  greater  inclination,  the  ball  will, 
of  course,  roll  more  rapidly  and  our  unit  of  space  will  in- 
crease from  one  foot,  as  supposed  thus  far,  to  two,  three, 
four  or  five  feet,  and  so  on,  but  the  number  of  such  spaces 
will  remain  as  indicated  in  the  table  above.  By  disre- 
garding the  resistance  of  the  air,  we  may  say  that  when 
the  plane  becomes  vertical,  the  body  becomes  a  freely 
falling  body.  Our  unit  of  space  has  now  become  16.08  ft. 
or  4.9  m.  It  will  fall  this  distance  during  the  first  second, 
three  times  this  distance  during  the  next  second,  five  times 
this  distance  during  the  third  second,  and  so  on. 

127.  Increment  of  Velocity. — During  the  first 
second  the  freely  falling  body  will  gain  a  velocity 
of  32.16  feet.      It  will   make  a  like  gain  of  velocity 
during  each  subsequent  second 'of  its  fall.    This  distance 
is  therefore  called  the  increment  of  velocity  due  to  gravity, 
and  is  generally  represented  by  g  —  32.16  ft.  or  9.8  m. 

Note — This  value  must  not  be  forgotten. 

128.  Formulas  for  Falling  Bodies.— If  now  we 

represent  our  space  by  \g,  the  velocity  at  the  end  of  any 
second  by  v,  the  number  of  seconds  by  t,  the  spaces  fallen 
each  second  by  s,  and  the  total  space  fallen  through  by  S, 
we  shall  have  the  following  formulas  for  freely  falling 

bodies  : 

(1.)  v=gt  or  |f  x  2t. 

(2.)    *  =  te(2$-l). 
(3.)  S  =  ig&. 


64  FALLING  BODIES. 

129.  Laws  of  Falling  Bodies.— These  formulas 
may  be  translated  into  ordinary  language  as  follows : 

(1.)  The  velocity  of  a  freely  falling  body  at  the  end  of 
any  second  of  its  descent  is  equal  to  32.16  ft.  (9.8  m.)  mul- 
tiplied by  the  number  of  the  second. 

(2.)  The  distance  traversed  by  a  freely  falling  body 
during  any  second  of  its  descent  is  equal  to  16.08  ft.  (4.9  m.) 
multiplied  by  one  less  than  twice  the  number  of  seconds. 

(3.)  The  distance  traversed  by  a  freely-falling  body 
during  any  number  of  seconds  is  equal  to  16.08  ft.  (4.9  m.) 
multiplied  by  the  square  of  the  number  of  seconds. 

130.  For  Bodies  Rolling  Down  an  Inclined 
Plane. — If  the  body  be  rolling  down  an  inclined  plane 
instead  of  freely  falling,  of  course  the  increment  of  velocity 
will  be  less  than  32.16  ft.     The  formulas  above  given  may 
be  made  applicable  by  multiplying  the  value  of  g  by  the 
ratio  between  the  height  and  length  of  the  plane. 

131.  Initial   Velocity  of  Falling  Bodies.  - 

We  have  been  considering  bodies  falling  from  a  state  of 
rest,  gravity  being  the  only  force  that  produced  the  motion. 
But  a  body  may  be  thrown  downward  as  well  as  dropped. 
In  such  a  case,  the  effect  of  the  throw  must  be  added  to 
the  effect  of  gravity.  It  becomes  an  illustration  of  the 
first  case  under  Composition  of  Forces  (§  80),  the  resultant 
being  the  sum  of  the  components.  If  a  body  be  thrown 
downward  with  an  initial  velocity  of  fifty  feet  per  second, 
the  formulas  will  become  v  =  gt  +  50 ;  s  =>$£  (2t—l) 


132.  Ascending  Bodies. — In  the  consideration  of 
ascending  bodies  we  have  the  direct  opposite  of  the  laws  of 
falling  bodies.  When  a  body  is  thrown  downward,  gravity 


FALLING   BODIES.  65 

increases  its  velocity  every  second  by  the  quantity  g. 
When  a  body  is  thrown  upward,  gravity  diminishes  its 
velocity  every  second  by  the  same  quantity.  Hence  the 
time  of  its  ascent  will  be  found  by  dividing  its  initial 
velocity  by  g.  TJ^e  initial  velocity  of  a  body  that 
can  rise  against  the  force  of  gravity  for  a  given 
number  of  seconds  is  the  same  as  the  final  velocity 
of  a  body  that  has  been  falling  for  the  same 
number  of  seconds. 

(a.)  The  spaces  traversed  and  the  velocities  attained  during  suc- 
cessive seconds  will  be  the  same  in  the  ascent,  only  reversed  in 
order.  If  a  body  be  shot  upward  with  a  velocity  of  321.6  feet,  it 
•will  rise  for  ten  seconds,  when  it  will  fall  for  ten  seconds.  The 
tenth  second  of  its  ascent  will  correspond  to  the  first  of  its  descent, 
i.  e.,  the  space  traversed  during  these  two  seconds  will  be  the  same ; 
the  eighth  second  of  the  ascent  will  correspond  to  the  third  of  its 
descent  ;  the  end  of  the  eighth  second  of  its  ascent  will  correspond 
to  the  end  of  the  second  second  of  its  descent. 

133.  Projectiles. — Every  projectile  is  acted  upon  by 
three  forces : 

(1.)  The  impulsive  force,  whatever  it  may  be. 
(2.)  The  force  of  gravity. 
(3.)  The  resistance  of  the  air. 

134.  Random   or  Range. — The  horizontal  dis- 
tance from   the   starting-point   of    a    projectile  to 
ivhere  it  strikes   the  ground   is   called   its  random 
or  range.    In  Fig.  30,  the  line  GE  represents  ^he  ran- 
dom of  a  projectile   starting  from   F,  and  striking  the 
ground  at  E. 

135.  Path  of  a  Projectile.— The  path  of  a  pro- 
jectile is  a  curve,  the  resultant  of  the  three  forces  above 
mentioned.     Suppose  a  ball  to  be  thrown   horizontally. 
Its  impulsive  force  will  give  a  uniform  velocity,  and  may 


66 


FALLING    BODIES. 


be  represented  by  a  horizontal   line   divided  into  equaJ 
parts,  each  part  representing  a  space  equal  to  the  velocity. 

The  force   of    gravity   may  be 

/>  fi  /•  J\  yv  -^ 

represented  by  a  vertical  line 
divided  into  unequal  parts, 
representing  the  spaces  1, 3>  5,  7. 
etc.,  over  which  gravity  would 
move  it  in  successive  seconds. 
Constructing  the  parallelograms 
of  forces,  we  find  that  at  the 
16  end  of  the  first  second  the  ball 
will  be  at  A,  at  the  end  of  the 
next  second  at  B,  at  the  end  of 
the  third  at  C,  at  the  end  of  the 
25  fourth  at  D,  etc.  The  result- 
ant of  these  two  forces  is  a  curve 
called  a  parabola.  It  will  be  seen  that,  in  a  case  like  this, 
the  range  GE  may  be  found  by  multiplying  the  velocity 
by  the  number  of  seconds  it  will  take  the  body  to  fall 
from  F  to  G.  The  resistance  of  the  air  modifies  the 
nature  of  the  curve  somewhat. 

136.  Time  of  a  Projectile.— From  the  second 
law  of  motion,  it  follows  that  the  ball  shot  horizontally 
will  reach  the  level  ground  in  the  same  time  as  if  it  had 
been  dropped ;  that  the  ball  shot  obliquely  upward  from  a 
horizontal  plain  will  reach  the  ground  in  twice  the  time 
required  to  fall  from  the  highest  point  reached.  These 
statements  may  be  easily  verified  by  experiment. 


FIG.  30. 


FALLING   BODIES.  67 


EXERCISES. 

1.  What  will  be  the  velocity  of  a  body  after  it  has  fallen  4 
seconds  ? 

Solution :  v  =  gt. 

v  =  32.16x4. 

v  =  128.64.  Ans.  128.64  ft. 

2.  A  body  falls  for  several  seconds ;    during  one  it  passes  ovel 
530.64  feet ;  which  one  is  it? 

Solution, :.  s  =  ^g  (2t  —  1). 

530.64  =  16.08  x  (2t  -  1). 

33  =  %t  -  1. 

34  =  2*. 

17  =  t.  Ans.  17th  second. 

3.  A  body  was  projected  vertically  upward  with  a  velocity  =  96.48 
feet ;  how  high  did  it  rise  ? 

Solution  :  v  =  gt.    (See  §  132.) 

96.48  =  32.16*. 
3  =  *. 
8=  fa*. 
8  =  16.08  x  9. 
S  =  144.72.  Ans.  144.72  ft. 

4.  How  far  will  a  body  fall  during  the  third  second  of  its  fall  ? 

5.  How  far  will  a  body  fall  in  10  seconds  ?  Ans.  1608  ft. 

6.  How  far  in  |  second?  Am.  4.02  ft. 

7.  How  far  will  a  body  fall  during  the  first  one  and  a  half  seconds 
of  its  fall  ? 

8.  How  far  in  12^  seconds  ? 

9.  A  body  passed  over  787.93  feet  during  its  fall ;   what  was  the 
ttme  required  ?  Ans.  7  sec. 

10.  What  velocity  did  it  finally  obtain  ? 

11.  A  body  fell  during  15i  seconds  ;  give  its  final  velocity. 

12."  In  an  Attwood's  machine  the  weights  carried  by  the  thread 
are  G|  ounces  each.  The  friction  is  equivalent  to  a  weight  of  two 
ounces.  When  the  "rider,"  which  weighs  one  ounce,  is  in  position, 
what  will  be  its  gain  in  velocity  per  second  ?  Ans.  2.01  ft. 

13.  A  stone  is  thrown  horizontally  from  the  top  of  a  tower 
257.28  ft.  high  with  a  velocity  of  60  ft.  a  second.  Where  will  it 
strike  the  ground?  Ans.  240  ft.  from  the  tower. 


68  FALLING  BODIES. 

14.  A  body  falls  freely  for  6  seconds.    What  is  the  space  trav; 
ersed  during  the  last  2  seconds  of  its  fall  ? 

15.  A  body  is  thrown  directly  upward  with  a  velocity  of  80.4  ft. 
(a)  What  will  be  its  velocity  at  the  end  of  8  seconds,  and  (&)  in  what 
direction  will  it  be  moving  ? 

16.  In  Fig.  30,  what  is  represented  by  the  following  lines :  Fl ! 
Fa?  Aa?  Fc?  Dd? 

17.  A  body  falls  357.28  ft.  in  4  seconds.    What  was  its  initial 
velocity  ?  Ans.  25  ft. 

18.  A  ball  thrown  downward  with  a  velocity  of  35  ft.  per  second 
reaches  the  earth  in  12^  seconds,      (a)  How  far  has  it  moved,  and 
(&)  what  is  its  final  velocity  ? 

19.  (a)   How  long  will  a  ball  projected  upward  with  a  velocity  of 
3,216  ft.  continue  to  rise  ?     (6)   What  will  be  its  velocity  at  the 
end  of  the  fourth  second  ?    (c)    At  the  end  of  the  seventh  ? 

20.  A  ball  is  shot  from  a  gun  with  a  horizontal  velocity  of  1,000 
feet,  at  such  an  angle  that  the  highest  point  in  its  flight  =  257.28 
feet.     What  is  its  random  ?  Ans.  8000  ft. 

21.  A  body  was  projected  vertically  downward  with  a  velocity  of 
10  feet ;  it  was  5  seconds  falling.     Required  the  entire  space  passed 
over.  Ans.  452ft. 

22.  Required  the  final  velocity  of  the  same  body.    Ans.  170.8  ft. 

23.  A  body  was  5  seconds  rolling  down  an  inclined  plane  and 
passed  over  7  feet  during  the  first  second,      (a)  Give  the  entire 
space  passed  over,  and  (6)  the  final  velocity. 

O  24.  A  body  rolling  down  an  inclined  plane  has  at  the  end  of  the 
first  second  a  velocity  of  20  feet ;  (a)  what  space  would  it  pass 
over  in  10  seconds?  (6)  If  the  height  of  the  plane  was  800  ft., 
what  was  its  length  ?  Last  Ans.  1286.4ft. 

25.  A  body  was  projected  vertically  upward  and  rose  1302.48  feet; 
give  (a)  the  time  required  for  its  ascent,  (6)  also  the  initial  velocity. 

26.  A  body  projected  vertically  downward  has  at  the  end  of  the 
seventh  second  a  velocity  of  235.12  feet ;  how  many  feet  will  it  have 
passed  over  during  the  first  4  seconds  ?  Ans.  297.28  ft. 

27.  A  body  falls  from  a  certain  height  ;    3  seconds  after  it  has 
started,  another  body  falls  from  the  height  of  787.92  feet;    from 
what  height  must  the  first  fall  if  both  are  to  reach  the  ground  at 
the  same  instant  ?  Ans.  1608  ft 

Recapitulation,— To  be  amplified  by  the  pupil  for 
review, 


PENDULUM.  69 


f  ACTED   UPON   BY   A   CONSTANT   FORCE 
RELATION    OF   WEIGHT   TO   VELOCITY. 

ILLUSTRATIVE  (     Galileo's, 


rf) 

w 

APPARATUS     |  Experiments   \  Results  tabulated. 
LAWS.  ...,.-{  INCREMENT   OP    VELOCITY  WITH  (unimpeded 

^    ^  FALL.  /  Impeded. 


EXPRESSED 


EFFECT   OF   INITIAL   VELOCITY. 


Ordinary  language. 


RELATIONS  TO 


(Ascending  bodies 


?!»*— 


IV. 


THE    PENDU  LU  M. 

137.  The   Simple  Pendulum.  —  A   simple  pen- 
dulum is  conceived  as  a  single  material  particle  sup- 
ported by  a  line  without  weight,  capable  of  oscillat- 
ing about  a  fixed  point.      Such   a  pendulum  has   a 
theoretical  but  not  an  actual  existence,  and  has  been  con- 
ceived for  the  purpose  of  arriving  at  the  laws  of  the  com- 
pound pendulum. 

138.  The    Compound    Pendulum.  —  A    com- 
pound or  physical  pendulum  is  a  iveight  so  suspended 
as  to  be  capable  of  oscillating  about  a  fixed  point. 
The  compound  pendulum  appears  in  many  forms.     The 
most  common  form  consists  of  a  steel  rod,  thin  and  flexible 
at  the  top,  carrying  at  the  bottom  a  heavy  mass  of  metal 
known  as  the  bob.     The  bob  is  sometimes  spherical  but 
generally  lenticular,  as  this  form  is  less  subject  to  resistance 
from  the  air. 


70 


THE  PENDULUM. 


FIG.  31. 


139.  Motion    of  the    Pendulum.— When    the 

supporting  thread  or  bar  is  vertical,  the  centre  of  gravity 
is  in  the  lowest  possible  position, 
and  the  pendulum  remains  at 
rest,  for  the  force  of  gravity  tends 
to  draw  it  downward  producing 
pressure  at  the  point  of  support, 
but  no  motion.  But  when  the 
pendulum  is  drawn  from  its  ver- 
tical position,  the  force  of  grav- 
ity, MG,  is  resolved  (§  91)  into 
two  components,  one  of  which, 
MO,  produces  pressure  at  the 
point  of  support,  while  the  other, 
MH,  acts  at  right  angles  to  it, 
producing  motion.  Gravity  there- 
fore draws  it  to  a  vertical  position,  when  inertia  carries  it 
beyond  until  it  is  stopped  and  drawn  back  again  by  grav- 
ity. It  thus  swings  to  and  fro  in  an  arc,  MNO. 

140.  Definitions. — The  motion  from  one  extremity 
of  this  arc  to  the  other  is  called  a  vibration  or  oscillation. 
The  time  occupied  in  moving  over  this  arc  is  called  the 
time  of  vibration  or  oscillation.    The  angle  measured  by 
this  arc  is  called  the  amplitude  of  vibration.     The  trip 
from   M    to  0  is   a  vibration;    the  angle  MAO   is   the 
amplitude  of  vibration. 

141.  Centre  of  Oscillation. — A  short  pendulum 
vibrates  more  rapidly  than  a  long  pendulum  ;    this  is  a 
familiar  fact.     It  is  evident,  then,  that  in  every  pendulum 
(not  simple)  the  parts  nearest  the  centre  of  suspension  tend 
to  move  faster  than  those  further  away,  and  force  them  to 


THE  PENDULUM.  71 

move  more  rapidly  than  they  otherwise  would.  On  the 
other  hand,  the  parts  furthest  from  the  centre  of  suspen- 
sion tend  to  move  more  slowly  than  those  nearer,  and  force 
these  to  retard  their  individual  rates  of  motion.  Between 
these  there  will  be  a  particle  moving,  of  its  own  accord, 
at  the  average  rate  of  all.  The  accelerating  tendency  of 
the  particles  above  it  is  compensated  by  the  retarding  ten- 
dency of  the  particles  below  it.  This  molecule,  there- 
fore, will  move  as  if  it  were  vibrating  alone,  sup- 
ported ~by  a  thread  without  weight.  It  fulfills  all  the 
conditions  of  a  simple  pendulum.  This  point  is  called  the 
centre  of  oscillation. 

142.  The  Real  Length  of  a  Pendulum.— The 

laws  of  the  simple  pendulum  are  applicable  to  the  com- 
pound pendulum  if  we  consider  the  length  of  the  latter  to 
be  the  length  of  the  equivalent  simple  pendulum,  i.  e.,  the 
distance  between  the  centres  of  suspension  and 
oscillation.  We,  therefore,  may  say  that  the  real  length 
of  a  pendulum  is  the  distance  between  the  centre  of  sus- 
pension and  the  centre  of  oscillation.  The  real  length  is 
less  than  the  apparent  length  except  in  the  imaginary  case 
of  the  simple  pendulum. 

143.  First  Law  of  the  Pendulum.— The  vi- 
brations of  a  given  pendulum,  at  any  given  place, 
are    isochronous,  i.  e.,  are  performed  in  equal  times, 
whether  the  arc  be  long  or  short.    Each  pupil   should 
satisfy  himself  of  the  truth  of  this  proposition,  by  the  only 
true  scientific  method,  experiment. 

144.  The    Cycloidal    Pendulum.  —  The   law 

above  given  is  strictly  true  only  when   the  pendu- 


THE  PENfiULUM. 


FIG.  32. 


lum  vibrates  in  a  cycloidal   arc.     A  cycloid  is  the 

curve  traced  by  a  point 
in  the  circumference 
of  a  circle  that  is  rolling 
along  a  straight  line. 
The  pendulum  maybe 
made  to  move  in  such 
an  arc  by  suspending 
a  small  heavy  ball  by 
a  thread  between  two 
cheeks  upon  which  the 

thread  winds  as  the  pendulum  vibrates.  The  cheeks  must 
be  the  two  halves  of  a  cycloid ;  each  cheek  must  have  the 
same  length  as  the  thread.  The  path  of  the  ball  will  be 
a  cycloid,  identical  with  that  to  which  the  cheeks  belong. 

(a.)  The  cycloidal  pendulum  is  of  little  practical  use.  If  the 
amplitude  of  an  ordinary  pendulum  does  not  exceed  five  degrees, 
the  circular  arc,  thus  described,  will  not  vary  much  from  the  true 
cycloidal  arc,  and  the  pendulum  will  be  practi- 
cally isochronous.  If  from  the  centre  of  sus- 
pension, with  radius  equal  to  the  length  of  the 
string,  a  circular  arc  be  described,  the  two 
curves  will  sensibly  coincide  for  at  least  five 
degrees.  This  is  why  the  pendulums  of  "  reg- 
ulator "  clocks  have  a  small  swing  or  amplitude. 

145.  Second  Law  of  the  Pen- 
dulum.— The  time  of  vibration  is 
independent  of  the  weight  or  mate- 
rial of  the  pendulum,  depending  only 
upon  the  length  of  the  pendulum,  and 
the  intensity  of  the  force  of  gravity  at 
any  given  place. 

(#.)  Each  pupil  should  try  the  experiment, 
ttt  home,  with  balls  of  equal  size  but  different  FIG.  33. 


THE  PENDULUM. 


weight.    The  investment  of  a  little  time  and  ingenuity  in  simple 
experiments  will  pay  large  dividends. 

146.  Third  Law  of  the  Pendulum.— The  vibra- 
tions of  pendulums  of  different  lengths  are  performed  in 
different  times.     The  lengths  are  directly  proportional 
to  the  squares  of   the  times  of   vibration,   or    in- 
versely proportional  to  the  squares  of  the  numbers 
of  vibrations  in  a  given  time. 

Note. — Be  careful  to  distinguish  clearly  hetween  the  expressions 
"times  of  vibration"  and  "numbers  of  vibration."  The  greater 
the  time,  the  less  the  number.  You  may  easily 
verify  by  experiment  the  three  laws  already 
given  for  the  pendulum. 

147.  The  Second's  Pendulum. 

At  the  equator,  the  length  of  a  second's 
pendulum,  at  the  level  of  the  sea,  is 
39  inches ;  near  the  poles,  39.2 ;  in  this 
latitude  about  39.1  inches  or  993.3 
mm.  As  such  a  pendulum  would  be 
inconveniently  long,  use  is  generally  made 
of  one  one-fourth  as  long,  which,  con- 
sequently, vibrates  half  seconds.  The 
length  and  time  of  vibration  of  this 
pendulum  being  thus  known,  the 
length  of  any  other  pendulum  may  be 
found  when  the  time  of  vibration  is 
given ;  or  the  time  of  vibration  may  be 
found  when  the  length  is  given.  The 
third  law  is  applicable  to  such  a  problem. 

148.  Use  of  the  Pendulum  in 
Time-pieces. — The  motion  of  a  clock  is  due  to  the 
force  of  gravity  acting  upon  the  weights,  or  to  the  elastic- 


FIG. 


PffE  PENDULUM. 


ity  of  the  spring.  But  the  weights  have  a  tendency  toward 
accelerated  motion  (falling  bodies),  while  the  spring  would 
give  an  example  of  diminishing  motion.  Either  defect 
would  be  fatal  in  a  time-piece.  Hence  the  properties  of 
the  pendulum  set  forth  in  the  first  and  third  laws  are 
used  to  regulate  this  motion  and  make  it  available  for  the 
desired  end.  If  the  clock  gains  time,  the  pendulum  is 
lengthened  by  lowering  the  bob;  if  it  loses  time,  the  pen- 
dulum is  shortened  by  raising  the  bob. 

149.  Compensation  Pendulums.— The  expan- 
sion of  metals  by  heat  is  a  familiar  fact.  Hence  the  ten- 
dency of  a  clock  to  lose  time  in  summer  and 
to  gain  time  in  winter.  One  plan  for  coun- 
teracting this  tendency  is  by  the  use  of  the 
"  gridiron  "  pendulum  which  is  made  of  twc 
substances  in  such  a  manner  that  the  down- 
ward  expansion  of  one  will  be  exactly  com« 
pensated  by  the  upward  expansion  of  tho 
other.  In  the  figure,  the  heavy  single  lines 
represent  steel  rods,  the  effect  of  whose  ex- 
pansion will  be  to  lower  the  bob.  The  light 
double  lines  represent  brass  rods,  the  effect  of 
whose  expansion  will  be  to  raise  the  bob.  The 
steel  rod  to  which  the  bob  is  directly  attached 
passes  easily  through  holes  in  the  two  hori- 
zontal bars  which  carry  the  brass  uprights. 


FIG.  35. 


As  brass  expands  more  than  steel,  for  a  given  increase  of 
temperature,  it  will  be  seen  that  these  two  expansions  may 
be  niiwle  to  neutralize  one  another. 


PENDULUM. 


EXERCISES. 


No. 

INCHES. 

NUMBER. 

TIME. 

No. 

C*. 

NUMBER. 

TIME. 

1 

9 

20  per  min. 

?- 

11 

99.33 

? 

? 

2 

? 

30       " 

? 

12 

? 

? 

2  sea 

3 

30 

? 

? 

13 

? 

f 

2  min. 

4 

16 

I 

? 

14 

24.83 

? 

? 

5 

f 

? 

£  sec. 

15 

? 

8  per  sec. 

? 

6 

? 

? 

£min. 

16 

397.32 

? 

? 

7 

39.37 

?  per  min. 

? 

17 

11.03 

? 

? 

8 

? 

10      " 

? 

1& 

1 

? 

10  sec. 

9 

10 

?  per  sec. 

? 

19 

2483.25 

? 

? 

10 

9 

1  per  min. 

? 

20 

? 

? 

4  sec. 

21.  How  will  the  times  of  vibration  of  two  pendulums  compare, 
their  lengths  being  4  feet  and  49  feet  respectively  ?    Ans.  As  2  to  7. 

22.  Of  two  pendulums,  one  makes  70  vibrations  a  minute,  the 
other  80  vibrations  during  the  same  time  ;    how  do  their  lengths 
compare?  Ana.  As  49  to  64. 

23.  If  one  pendulum  is  4  times  as  long  as  another,  what  will  be 
their  relative  times  of  vibration  ? 

24.  The  length  of  a  second's  pendulum  being  39.1  inches,  what 
must  be  the  length  of  a  pendulum  to  vibrate  in  ^  second  ? 

25.  How  long  must  a  pendulum  be  to  vibrate  once  in  8  seconds ! 
In  |  second  ? 

26.  How  long  must  a  pendulum  be  to  vibrate  once  in  3|^  seconds  ? 

27.  Find  the  length  of  a  pendulum  that  will  vibrate  5  times  in  4 
seconds  ?  Ans.  25.02  +  inches. 

28.  A  pendulum  5  feet  long  makes  400  vibrations  during  a  certain 
time  ;  how  many  vibrations  will  it  make  in  the  same  time  after  the 
pendulum  rod  has  expanded  half  an  inch  ? 

Recapitulation. — In  this  section  we  have  considered 
Lhe  Simple  Pendulum  ;  the  Compound  Pen- 
dulum ;  the  nature  of  the  Motion  of  the  Pendu~ 
lum  and  its  Cause  ;  the  meaning  of  the  terms  Vi- 
bration, Time  of  Vibration,  Amplitude  of 
Vibration;  Centre  of  Oscillation;  Real  Length 


ENERGY. 


of  a  Pendulum  ;  Laws  and  Formulas  for  the  Pen- 
dulum ;  the  Cyeloidal  Pendulum;  the  Second's 
Pendulum  ;  the  Use  of  the  Pendulum  in  Clock- 
work; Compensation  Pendulums. 


ECTION    V. 


ENERGY, 

150.  Work. — In   physical  science,  the   word   ivork 
signifies  the  overcoming   of  resistance  of  any  kind. 
Whether  this  overcoming  of  resistance  is  pleasant  or  not 
does  not  enter  into  consideration  here,  all  play  being  a 
species  of  ivork.     The  word  is  here  used  in  this  technical 
sense.     When  a  force  causes  motion  through  space,  it  is 
said  to  do  work.     The  product  of  the  force  acting  and  the 
space  through  which  the  body  is  moved  measures  the  work 
done  on  that  body.     Work  implies  a  change  of  position 
and  is  independent  of  the  time  taken  to  do  it. 

151.  Energy.  —  Energy  is  the   power  of  doing 
work.    If  one  man  can  do  more  work  than  another,  he 
has  more  energy.     If  a  horse  can  do  more  work,  in  a  given 
time,  than  a  man,  the  horse  has  more  energy  than  the  man. 
If  a  steam-engine  can  do  more  work  than  a  horse,  it  has 
more  energy.    If  a  moving  cannon-ball  can  overcome  a 
greater  resistance  than  a  base-ball  it  has  more  energy. 

152.  Elements  of  Work  Measure. — Imagine  a 
flight  of  stairs,  each  step  having  a  rise  of  twelve  inches. 
On  the  floor  at  the  foot  of  the  stairs  are  two  weights,  of 


ENERGY.  11 

one  and  ten  pounds  respectively.  Lift  the  first  weight  to 
the  top  of  the  first  step.  How  much  work  have  you  per- 
formed ?  Perhaps  you  will  answer,  one  pound  of  work, 
Now  place  the  second  weight  beside  the  first.  How  much 
work  did  you  perform  in  so  doing  ?  Perhaps  you  will  say 
ten  times  as  much  as  before,  or  ten  pounds.  Now  lift 
each  of  them  another  step,  and  then  another,  until  they 
rest  on  the  top  of  the  tenth  step.  To  lift  the  heavier 
weight  the  second,  third,  and  subsequent  times  involved 
each  as  much  work  as  to  lift  it  the  first  foot,  but  you 
would  hardly  say  that  you  had  lifted  a  hundred  pounds. 
Still  it  is  sure  that  to  place  it  on  the  tenth  step  required 
just  ten  times  as  much  work  as  it  did  to  place  it  on  the  first 
step,  or  just  one  hundred  times  as  much  work  as  it  did  to 
place  the  one  pound  weight  on  the  first  step.  Moreover, 
it  is  evident  that  the  two  elements  of  weight  and 
height  are  necessarily  to  be  considered  in  measuring 
the  work  actually  performed. 

153.  Units   of  Work;    the  Foot-pound.— It 

is  often  necessary  to  represent  work  numerically;  hence 
the  necessity  for  a  unit  of  measurement.  The  unit  com- 
monly in  use,  for  the  present,  in  England  and  this  country 
is  the  foot-pound.  A  foot-pound  is  the  amount  of  work 
required  to  raise  one  pound  one  foot  high  against 
the  force  of  gravity.  The  work  required  to  raise  one  kilo- 
gram one  meter  high  against  the  same  force  is  called  a 
kilogram-meter. 

(a.)  To  get  a  numerical  estimate  of  work,  we  multiply  the  numbe* 
of  weight  units  raised  by  the  number  of  linear  units  in  the  vertical 
height  through  which  the  body  is  raised.  A  weight  of  2^  pounds, 
raised  3  feet,  or  one  of  3  pounds  raised  25  feet,  represents  75  foot* 
pounds.  A  weight  of  15  Kg.  raised  10  m.,  represents 
meters. 


78  ENERGY. 

154.  The  Erg.— The  C.  G.  S.  (or  absolute)  unit  of 
work  is  called  the  erg.    It  is  the  work  done  in  moving 
rt  free  body  one  centimeter  against  a  force  of  one 
dyne  (§  69).     The  work  of  lifting  one  gram  one  centi- 
meter against  the  force  of  gravity  is  980  ergs.     A  foot- 
pound is  about  13,560,000  ergs.  , 

(a.)  The  definition  of  erg  points  out  the  fact  that  work  equals 
force  multiplied,  by  distance. 

155.  Horse -Power. — The  rate  of  doing  work  is 
called  power.    A  horse-power  represents  the  ability  to 
perform  550  foot-pounds  in  a  second  or  33,000  foot- 
pounds in  a  minute.   It  equals  746  x  107  ergs  per  second. 

(a.)  An  engine  that  can  do  66,000  foot-pounds  in  a  minute  or 
33,000  foot-pounds  in  half  a  minute  is  called  a  two  horse-power 
engine.  To  compute  the  number  of  horse-powers  represented  by  an 
engine  at  work,  multiply  the  number  of  pounds  raised  by  the  num- 
ber of  feet,  and  divide  the  product  by  550  times  the  number  of  seconds 
or  33,000  times  the  number  of  minutes  required  to  do  the  work. 

156.  Relation  of  Velocity  to  Energy.— Any 

moving  body  can  overcome  resistance  or  perform  work ; 
it  has  energy.  We  must  acquire  the  ability  to  measure  this 
energy.  In  the  first  place,  we  may  notice  that  the  direc- 
tion of  the  motion  is  unimportant.  A  body  of  given 
weight  and  velocity  can,  at  any  instant,  do  as  much  work 
when  going  in  one  direction  as  when  going  in  another. 
This  energy  may  be  expended  in  penetrating  an  earth- 
bank,  knocking  down  a  wall  or  lifting  itself  against  the 
force  of  gravity.  Whatever  be  the  work  actually  done,  it 
is  clear  that  the  manner  of  expenditure  does  not  change 
the  amount  of  energy  expended.  We  may,  therefore, 
find  to  what  vertical  height  the  given  velocity 
would  lift  the  body,  and  thus  easily  determine  its 
energy  in  foot-pounds,  kilo^ramTn^t&rs  or  dynes, 


ENERGY.  79 

157.  An  Easier  Method. — If  we  can  obtain  the 

same  result  without  the  trouble  of  finding  how  high  the 
given  velocity  could  raise  it,  it  is  generally  desirable  to  do 
so.  Our  vertical  height  is  the  whole  space  passed  over  by 
an  ascending  body  (§  132).  We  have  given  v  to  find  8. 

gt  =  v. 

t=V-. 
9 

Substituting  the  above  value  of  tf8,  we  have, 


Energy  =  wS  (the  weight  into  the  height).  Substitut- 
ing our  new  value  for  $,  we  have  the  following  important 
formula  : 

Kinetic  Energy  =  ^. 
^g 

Since  the  weight  of  a  body  results  from  its  mass  and  the 
force  of  gravity  (w  =  mg\ 

Kinetic  Energy  =  \ 


(a.}  If  w  be  given  in  pounds  ;  u,  in  feet  per  second  and  g  in  feet, 
the  first  formula  will  give  the  value  of  K.  E.  in  foot-pounds. 

(6.)  If  the  gram  be  taken  as  the  unit  of  mass  and  the  centimeter 
per  second  as  the  unit  of  velocity,  the  second  formula  will  give  the 
value  of  K.  E.  in  ergs. 

158.  Two  Types  of  Energy.  —  There  are  two  types 
of  energy  .which  may  be  designated  as  energy  of  motion 
and  energy  of  position.  With  the  first  of  these  we  are 
familiar.  A  falling  weight  or  running  stream  possesses 
energy  of  motion  ;  it  is  able  to  overcome  resistance  by 
reason  of  its  weight  and  velocity.  On  the  other  hand, 
before  the  weight  began  to  fall,  while,  as  yet,  it  had  no 


80  ENERGY. 

motion  but  was  at  rest,  it  had  the  power  of  doing  work  by 
reason  of  its  elevated  position  with  reference  to  the  earth. 
When  the  water  of  the  running  stream  was  at  rest  in  the 
lake  among  the  hills  it  had  a  power  of  doing  work,  an 
energy,  which  was  not  possessed  by  the  waters  of  the 
pond  in  the  valley  below.  This  energy  or  power  results 
from  its  peculiar  position.  Energy  of  motion  is  called 
kinetic  energy;  energy  of  position  is  called  potential 
energy. 

159.  Convertibility  of  Kinetic  and  Poten- 
tial Energies. — "We  may  at  any  moment  convert  kinetic 
energy  into  potential,  or  potential  energy  into  kinetic. 
One  is  as  real  as  the  other,  and  when  it  exists  at  all,  exists 
at  the  expense  of  a  definite  amount  of  the  other.  Imagine 
a  ball  thrown  upward  with  a  velocity  of  64.32  feet.  As  it 
begins  to  rise  it  has  a  certain  amount  of  kinetic  energy. 
At  the  end  of  one  second  it  has  a  velocity  of  only  32.16  ft 
Consequently  its  kinetic  energy  has  diminished.  But 
it  has  risen  48.24  ft.,  and  has  already  a  considerable  poten- 
tial energy.  All  of  this  potential  energy  results  from  the 
kinetic  energy  which  has  disappeared.  At  the  end  of 
another  second,  the  ball  has  no  velocity;  it  has  reached  the 
turning-point  and  is  at  rest.  Consequently,  it  has  no 
kinetic  energy.  But  the  energy  with  which  it  began  its 
flight  has  not  been  annihilated ;  it  has  been  stored  up  in 
the  ball  at  a  height  of  64.32  ft.  as  potential  energy.  If  at 
this  instant  the  ball  be  caught,  all  of  the  energy  may  be 
kept  in  store  as  potential  energy.  If  now  the  ball  be 
dropped,  it  begins  to  lose  its  potential  and  to  gain  kinetic 
energy.  When  it  reaches  the  ground  at  the  end  of  two 
seconds  it  has  no  potential  energy,  "but  just  ay  much  of  the 


ENERGY. 


kinetic  type  as  was  given  to  it  when  it  began  to  rise.  This 
illustrates  in  a  simple  way  the  important  principle,  the 
transformation  or  convertibility  of  energy  without 
any  change  in  its  quantity. 

160.  Energy   a   Constant    Quantity.— In  the 

case  of  the  ball  thrown  upward,  at  the  start,  at  the  finish, 
or  at  any  intermediate  point  of  either  its  ascent  or  descent, 
the  sum  of  the  two  types  of  energy  is  the  same.  It  may 
be  all  kinetic,  all  potential,  or  partly  both.  In  any  case, 
the  swin  of  the  two  continually  varying  energies  is 
constant.  Just  as  a  man  may  have  a  hundred  gold  dol- 
lars, now  in  his  hand,  now  in  his  pocket,  now  part  in  his 
hand  and  the  rest  in  his  pocket ;  changing  a  dollar  at  a 
time  from  hand  to  pocket  or  vice  versa,  the  amount  of 
money  in  his  possession  remains  constant,  viz.,  one  hun- 
dred dollars. 

161.  Pendulum    Illustration.— The    pendulum 
affords  a  good  and  simple  illustration  of  kinetic  and  poten- 
tial energy,  their  equivalence 

and  convertibility.  When  the 
pendulum  hangs  at  rest  in  a 
vertical-  position,  as  P#,  it  has 
no  energy  at  all.  Considered  as 
a  mass  of  matter,  separated  from 
the  earth,  it  certainly  has  po- 
tential energy;  but  considered 
as  a  pendulum, it  has  no  energy. 
If  the  pendulum  be  drawn 
aside  to  5,  we  raise  it  through 
the  space  ah  ;  that  is,  we  do 
work,  or  spend  kinetic  energy  upon  it.  The  energy  thus 


82  ENERGY. 

expended  is  now  stored  up  as  potential  energy,  ready  to  be 
reconverted  into  energy  of  the  kinetic  type,  whenever  we 
let  it  drop.  As  it  falls  the  distance  ha,  in  passing  from  b 
to  a,  this  reconversion  is  gradually  going  on.  When  the 
pendulum  reaches  a  its  energy  is  all  kinetic,  and  just  equal 
to  that  spent  in  mi  sing  it  from  a  to  I.  This  kinetic  energy 
now  carries  it  on  to  c,  lifting  it  again  through  the  space  ah. 
Its  energy  is  again  all  potential  just  as  it  was  at  I.  If  we 
could  free  the  pendulum  from  the  resistances  of  the  air 
and  friction,  the  energy  originally  imparted  to  it  would 
swing  to  and  fro  between  the  extremes  of  all  potential  and 
all  kinetic;  but  at  every  instant,  or  at  every  point  of  the 
arc  traversed,  the  total  energy  would  be  an  unvarying 
quantity,  always  equal  to  the  energy  originally  exerted  in 
swinging  it  from  a  to  #. 

162.  Indestructibility  of  Energy.  —  From  the 
last  paragraph  it  will  be  seen  that,  were  it  not  for  friction 
and  the  resistance  of  the  air,  the  pendulum  would  vibrate 
forever  ;  that  the  energy  would  be  indestructible.  Energy 
is  withdrawn  from  the  pendulum  to  overcome  these  imped- 
iments, but  the  energy  thus  withdrawn  is  not  destroyed. 
What  becomes  of  it  will  be  seen  when  we  come  to  study 
heat  and  other  forms  of  energy,  which  result  from  the 
motions  and  positions  of  the  molecules  of  matter.  The 
truth  is  that  energy  is  as  indestructible  as  matter. 
For  the  present  we  must  admit  that  a  given  amount  of 
energy  may  disappear,  and  escape  our  search,  but  it  is  only 
for  the  present.  We  shall  soon  learn  to  recognize  the 
fugitive  even  in  disguise. 


.—  -Physics  may  now  be  defined  as  the  science  of  matter  and 
energy. 


ENERGY.  83 


EXERCISES. 

1.  How  many  horse-powers  in  an  engine  that  will  raise  8,250  Ibe. 
ITO  ft.  in  4  minutes  ? 

2.  A  ball  weighing  192.96  pounds  is  rolled  with  a  velocity  of  IOC 
feet  a  second.     How  much  energy  has  it?    Ans.  30000  foot-pounds, 

3.  A  projectile  weighing  50  Kg.  is  thrown  obliquely  upward  with 
a  velocity  of  19.6  in.     How  much  kinetic  energy  has  it  ? 

4.  A  ten-pound  weight  is  thrown  directly  upward  with  a  velocity 
of  225. 12  ft.     (a.)  What  will  be  its  kinetic  energy  at  the  end  of  the 
third  second  of  its  ascent?    (&.)  At  the  end  of  the  fourth  second  of 
its  descent  ? 

5.  A  body  weighing  40  Kg.  moves  at  the  rate  of  30  Km.  per  hour. 
Find  its  kinetic  energy. 

6.  What  is  the  horse  power  of  an  engine  that  can  raise  1,500 
pounds  2,376  feet  in  3  minutes?  Ans.  36  H.  P. 

7.  A  cubic  foot  of  water  weighs  about  62£  pounds.     What  is  the 
horse-power  of  an  engine  that  can  raise  300  cubic  feet  of   water 
every  minute  from  a  mine  132  ft.  deep  ? 

8.  A  body  weighing  100  pounds  moves  with  a  velocity  of  20  miles 
per  hour.     Find  its  kinetic  energy. 

9.  A  weight  of  3  tons  is  lifted  50  feet,    (a.)  How  much  work  was 
done  by  the  agent?    (6.)  If  the  work  was  done  in  a  half -minute, 
what  was  the  necessary  horse-power  of  the  agent  ? 

10.  How  long  will  it  take  a  two  horse-power  engine  to  raise  5 
tons  100  feet  ? 

11.  How  far  can  a  two  horse-power  engine  raise  5  tons  in  30  sec.  ? 

12.  What  is  the  horse-power  of  an  engine  that  can  do  1,650,000 
foot-pounds  of  work  in  a  minute  ? 

13.  What  is  the  horse-power  of  an  engine  that  can  raise  2,376 
pounds  1,000  feet  in  2  minutes  ? 

14.  If  a  perfect  sphere  rest  on  a  perfect,  horizontal  plane  in  a 
vacuum,  there  will  be  no  resistance  to  a  force  tending  to  move  it. 
How  much  work  is  necessary  to  give  to  such  a  sphere,  under  such 
circumstances,  a  velocity  of  20  feet  a  second,  if  the  sphere  weighs 
201  pounds  ?  Ans.  1250  foot-pounds. 

15.  A   railway  car  weighs  10  tons.     From  a  state  of  rest  it  is 
moved  50  feet,  when  it  is  moving  at  the  rate  of  3  miles  an  hour 
If  the  resistances  from  friction,  etc.,  are  8  pounds  per  ton,  how 
many  foot-pounds  of  work  have  been  expended  upon  the  car? 
(First  find  the  work  done  in  overcoming  friction,  etc.,  through  50  ft. 
which  is  50  foot-pounds  x  10  x  8.     To  this  add  the  work  done  in 
giving  the  car  kinetic  energy.) 


84  ENERGY. 

Recapitulation. — In  this  section  we  have  considered 
the  meaning  of  Work  and  Energy;  the  Ele- 
ments of  Work-measure;  the  Unit  of  Work,  as 
Foot-pound  or  Kilogram-meter ;  Horse- 
power; the  relation  between  Velocity  and  En- 
ergy ;  a  very  convenient  Formula  for  Energy  ; 
two  Types  of  Energy,  Kinetic  a. A!  Potential ; 
the  mutual  Convertibility  of  these  two  Types  of 
Energy ;  the  Sum  of  these  two  as  a  Constant  Quan- 
tity ;  the  Pendulum  as  an  Illustration  of  this  Con- 
vertibility and  Constancy;  the  Indestructibility  of 
Energy. 

REVIEW  QUESTIONS  AND  EXERCISES, 

1.  (a.)  What  is  a  molecule?    (&.)  An  atom?    (c.)  Name  the  attrae 
tions  pertaining  to  each. 

2.  (a.)  Give  an  original  illustration  of  a  physical  change.    (&.)  Of 
a  chemical  change. 

3.  (a.)  What  is  the  difference  between  general  and  characteristic 
properties  of  matter?    (&.)  Give  an  illustration  of  impenetrability, 
not  mentioned  in  the  book. 

4.  (a.)  Upon  what  property  do  most  of  the  characteristic  proper- 
ties of  matter  depend?    (b.)  Name  five  general  and  three  charac- 
teristic properties  of  matter,    (c.)  Define  inertia. 

5.  («.)  How  does  a  solid  differ  from  a  liquid?    (&.)  From  a  gas? 
(c.)  How  does  a  gas  differ  from  a  vapor  ?    (d.)  What  is  a  fluid  ? 

6.  (a.)  Define  dynamics.      (&.)  What  is  the  difference  between 
statics  and  kinetics?    (c.)  What  is  the  gravity  unit  of  force?    (d.) 
The  kinetic  unit  ? 

7.  («.)  Give  Newton's  Laws  of  Motion.     (&.)  Explain  the  meaning 
of  "parallelogram  of  forces."    (c.)  What  is  an  equilibrant  ?    (d.) 
Give  the  law  of  reflected  motion. 

8.  (a.)  What  is  the  difference  between  gravity  and  gravitation  ? 
(&.)  Give  the  law  of   gravitation,     (c.)  Of  weight,    (d.)  What  in 
meant  by  centre  of  gravity  ? 

9.  (a.)  Describe  the  several  kinds  of   equilibrium.     (&.)  Upon 
what  does  the  stability  of  a  body  depend?    (c.)  Show  how.    (d.} 
What  is  the  line  of  direction  ? 


ENERGY.  85 

10.  (a.)  Why  is  it  that  a  lead  ball  and  a  wooden  ball  will  fall  100 
feet  in  the  same  time  ?    (&.)  How  did  Galileo  study  the  laws  of 
falling  bodies  ?    (c.)  Who  was  Galileo  and  when  did  he  live?    (d.) 
Define  increment  of  velocity. 

11.  (a.)  Give  the  laws  of  freely  falling  bodies.     (&.)  Express  the 
same  truths  algebraically,    (c.)  What  forces  act  upon  a  projectile  ? 
(d.)  Define  random. 

12.  (a.)  What  is  a  simple  pendulum  ?     (6.)  A  compound  pen- 
dulum?   (c.)  What  is  the  real  length  of  a  pendulum?    (d.)  How 
long  must  a  pendulum  be  to  vibrate  once   a  minute  ?    (e.)  Once  a 
second  ?    (/. )  What  is  the  most  important  property  of  a  pendulum  ? 

13.  Two  forces  of  6  and  8  pounds  respectively  act  at  right  angles 
to  each  other.    Find  the  direction  and  intensity  of  their  equilibrant. 

14.  (a.)  Define  energy.     (&.)  Foot-pound,    (c.)  Horse-power,    (d.) 
Give  the  rule  for  calculating  horse-power. 

15.  (a.)  What  is  a  kilogram-meter?     (&.)  Give  the  formula  for 
the  calculation  of  kinetic  energy  from  weight  and  velocity,     (c.) 
Deduce  the  same. 

16.  (a.)  State  fully  and  clearly  the  difference  between  kinetic  and 
potential  energy.     (&.)  Illustrate  the  same  by  the  pendulum. 

17.  (a.)  What  is  the  object  of  experiments  in  the  study  of  phy- 
sics?   (&.)  What  is  the  metric  unit  of  weight?    (c.)  How  is  it  ob- 
tained ? 

*  18.  Three  inelastic  balls  weighing  5,  7  and  8  pounds,  lie  in  the 
same  straight  line.  The  first  strikes  the  second  with  a  velocity  of 
60  feet  per  second  ;  the  first  and  second  together  strike  the  third. 
What  will  be  the  velocity  of  the  third  ?  Ans.  15  ft. 

19.  To  how  many  F.  P.  S.  units  of  force  is  the  weight  of  9  Ib. 
equal  ? 

20.  To  how  many  C.  G.  S.  units  of  force  is  the  weight  of  9  Kg. 
equal  ? 

21.  How  many  ergs  will  represent  the  kinetic  energy  of  a  ball 
weighing  50  grams  and  moving  at  the  rate  of  60  cm.  a  second  ? 

Ans.  90,000. 

22.  Determine  the  amount  of  work  performed  in  discharging  a 
30  gram  bullet  with  a  velocity  of  400  m.  per  second. 

Ans.  24  x  108  ergs. 


V, 

SIMPLE    MACH  INES. 


ECTfON  I. 


PRINCIPLES    OF    MACHINERY.— THE    LEVER. 

163.  What   is  a  Machine?— </2  machine  is  a 
contrivance  by  means  of  which  the  force    can  be 
applied  to  the  resistance  jnore  advantageously.    Its 
general  office  is  to  effect  a  transformation  in  the  inten- 
sities of  energies,  so  that  an  energy  of  small  intensity, 
acting  through  a  considerable  distance,  may  be  made  to 
reappear  as  an  energy  of  considerable  intensity,  acting 
through  a  small  distance,  or  vice  versa. 

164.  A   Machine  cannot  Create   Energy.— 

No  machine  can  create  or  increase  energy.  In  fact,  the 
use  of  a  machine  is  accompanied  by  a  waste  of  power 
which  is  needed  to  overcome  the  resistances  of  friction,  the 
air,  etc.  A  part  of  the  energy  exerted  must  therefore  be 
used  upon  the  machine  itself,  thus  diminishing  the  amount 
that  can  be  transmitted  or  utilized  for  doing  the  work  in 
hand. 

165. — A  Common  Error. — A  clear  understanding 
of  this  fact  is  very  important.    There  is  a  very  common 


PRINCIPLES   OF  MACHINERY.  87 

erroneous  notion  that,  in  some  way  or  other,  a 
machine  performs  work  of  itself — that  it  is  a  source  of 
power.  It  were  as  reasonable  to  imagine  that  a  bank  is  a 
source  of  real  money.  The  bank  can  pay  out  no  more 
than  it  receives;  neither  can  a  machine.  A  man  may  go 
to  the  bank  with  a  ten-dollar  gold  piece,  and  get  for 
it  ten  one-dollar  gold  pieces.  In  like  manner,  he  may  gc 
to  a  machine  with  an  ability  of  moving  ten  pounds  one 
foot  in  a  given  time,  and  get  for  it  the  ability  of  moving 
one  pound  ten  feet  in  the  same  time.  He  may  exchange 
what  he  has  for  what  he  prefers  ;  but,  in  the  case  of  the 
bank  and  of  the  machine  alike,  the  equivalent  must  be 
paid,  and  generally  a  commission  for  the  transfer. 

166.  Of  what  Use  are  Machines  ?— Some  of  the 

many  advantages  resulting  from  the  use  of  machines  are : 

(1.)  It  enables  us  to  exchange  intensity  for  a  velocity 
otherwise  unattainable,  as  in  the  case  of  the  sewing 
machine  or  spinning  wheel. 

(2.)  It  enables  us  to  exchange  velocity  for*  an  intensity  of 
power  otherwise  unattainable,  as  in  the  case  of  lift- 
ing a  large  stone  with  a  crow-bar  or  pulleys. 

(3.)  It  enables  us  to  change  the  direction  of  our  force,  as 
in  the  case  of  hoisting  a  flag  on  a  flag-staff.  It 
would  be  inconvenient  to  climb  the  pole  and  then 
draw  up  the  flag. 

(4.)  It  enables  us  to  employ  other  forces  than  our  own,  as 
the  strength  of  animals,  the  forces  of  wind,  water, 
steam,  etc. 

167.  General  Laws  of  Machines.— The  work  to 
be  done  by  a  machine  is  generally  called  the  weight  or 
load.    The  force  applied  is  called  the  power.     The  work 


88  THE  LEVER. 

of  the  power  (e.  g.,  foot-pounds)  is  always  equal  to  the 
work  of  the  load,  the  work  expended  in  the  machine  itself 
being  disregarded.  The  following  laws  are,  therefore, 
applicable  to  machines  of  every  kind : 

(1.)  What  is  gained  in  intensity  of  power  is  lost 
in  time,  velocity,  or  distance;  and  what  is 
gained  m  time,  velocity,  or  distance  is  lost  in  inten- 
sity of  power. 

(2.)  The  power  multiplied  by  the  distance  through 
which  it  moves,  equals  the  weight  multiplied 
by  the  distance  through  which  it  moves. 

(3.)  The  power  multiplied  by  its  velocity,  equals  the 
weight  multiplied  by  its  velocity. 

168.  What  is  a  Lever? — A  lever  is  an  inflex- 
ible  bar  capable  of  being   freely    moved    about  a 
fixed  point  or  line,  called  the  fulcrum. 

In  every  lever,  three  points  are  to  be  considered,  viz.: 
the  fulcrum  and  the  points  of  application  for  the  power 
and  the  weight.  Every  lever  is  said  to  have  two  arms. 
The  power-arm  is  the  perpendicular  distance  from  the  ful- 
crum to  the  line  in  which  the  power  acts;  the  weight-arm 
is  the  perpendicular  distance  from  the  fulcrum  to  the  line 
in  which  the  weight  acts.  If  the  arms  are  not  in  the  same 
straight  line,  the  lever  is  called  a  bent  lever. 

169.  Classes  of  Levers. — There  are  three  classes 

of  levers,  depending  upon  the 
relative  positions  of  the  power, 
weight,  and  fulcrum. 

FIG.  37.  (1.)  If  the  fulcrum  is  be- 


THE  LEVER. 


89 


FTG.  38. 


tween  the  power  and  weight  (P.  F.  W.),  the  lever  is  of 
the  first  class  (Fig.  37);  e.  g.9  crowbar,  balance,  steelyard, 
scissors,  pincers. 

(2.)  If  the  weight  is  be- 
tween the  power  and  the 
fulcrum  (P.  W.  F.),  the 
lever  is  of  the  second  class 
(Fig.  38) ;  e.  g.,  cork-squeezer, 
nut-cracker,  wheel-barrow. 

(3.)    If   the  power  is  be-  f 

tween  the  weight  and  the  ful-   _ 
cram  (W.  P.  P.),  the  lever  is  *^=== 
of  the  third  class  (Fig.  39); 
e.  g.,  fire-tongs,  sheep-shears, 
human  fore-arm.  FlG'  39« 

17O.  Static  Laws  of  the  Lever.— It  will  be 
clearly  seen  or  may  be  geometrically  shown  that  the  ratio 
between  the  arms  of  the  lever  will  be  the  same  as  the  ratio 
between  the  velocities  of  the  power  and  the  weight,  and 
the  same  as  the  ratio  between  the  distances  moved  by  the 
power  and  the  weight.  If  the  power-arm  be  twice  as  long 
as  the  weight-arm,  the  power  will  move  twice  as  fast  and 
twice  as  far  as  the  weight  does.  The  general  laws  of  ma' 
chines  may  therefore  be  adapted  to  the  lever  as  follows  : 

P  x  power-arm  =  W  x  weight-arm,  or  P  x  PF  =  W  x  WP. 


/.  P  :  W  : :  W. F  :  PF. 

(I.)  In  the  case  of  the  lever,  the  power  and  weight  are 
inversely  proportional  to  the  corresponding  arms  of  the 
lever;  or, 


90  THE    LEVER. 

(2.)  The  power  multiplied  by  the  power-arm  equals  the 
weight  multiplied  by  the  weight-arm  ;  or, 

(3.)  A  given  power  will  support  a  weight  as  many 
times  as  great  as  itself,  as  the  power-arm  is  times  as 
long  as  the  weight-arm. 

Note. — A  static  law  expresses  the  relation  between  the  power  and 
weight  when  the  machine  is  in  equilibrium.  In  order  that  there  be 
motim,  one  of  the  products  mentioned  in  the  law  above  must  be 
greater  than  the  other.  The  lever  itself  must  be  in  equilibrium 
before  the  power  and  weight  are  applied.  It  is  to  be  noticed  that 
when  we  speak  of  the  power  multiplied  by  the  power-arm,  we  refer 
to  the  abstract  numbers  representing  the  power  and  power-arm. 
We  cannot  multiply  pounds  by  feet,  but  we  can  multiply  the  number 
of  pounds  by  the  number  of  feet. 

171.  The  Moment   of  a  Force.— The  moment 
of  a  force  acting  about  a  given  point,  as  the  fulcrum  of  a 
lever,  is  the  product  of  the  numbers  representing 
respectively   the  magnitude  of  the  force  and  the 
perpendicular   distance   between   the  given   point 
and   the   line   of  the   force.     In  the    case    of   the 
lever  represented   in    Fig.  37,  the  weight-arm  is  8  mm. 
and  the  power-arm  is  30  mm.    Suppose  that  the  power  is 
4  grams,  and  let  the  weight  be  represented  by  x.    Then 
the  moment  of  the  force  acting  on  the  power-arm  will  be 
represented  by  (4  x  30  =)  120,  and  the  moment  of  the 
force  acting  on  the  weight-arm  by  Sx. 

172.  Moments  Applied  to  the  Lever. — We 

sometimes  have  sev- 

ii^fc 
eral  forces    acting 
5     F         10 | 80  upon  one  or  both 

20] ijf~~  A  20  .         , 

J  J  e\  /      arms  of  a  lever,  in 

il        i        4          i  the  same  or  in 

40.  opposite  directions. 


THE  LEVER. 


91 


Cinder  such  circumstances,  the  lever  will  be  in  equilibrium, 
when  the  sum  of  the  moments  of  the  forces  tending  to 
turn  the  lever  in  one  direction  is  equal  to  the  sum  of  the 
moments  of  the  forces  tending  to  turn  the  lever  in  the 
other  direction.  Representing  the  moments  of  the  several 
forces  acting  upon  the  lever  represented  in  the  figure  by 
their  respective  letters  and  numerical  values, 

b+c+dzza+e+f        30+30  +  40  =  30  +  25+45. 
or,  c+d— a  =  e  +  f—l         30  +  40—30  =  25  +  45—30. 

173.  Bent    Levers. — When   the  lever   is  not  a 

straight  bar,  or  when,  for  any  reason,  the  power  and 

weight   do   not  act  parallel  to  each 

other,  it  becomes  necessary  to  distinguish 

between  the  real  and  apparent  arms  of  the 

lever.    This  will  be  easily  done,  if  you  are 

familiar  with  the  definition  of  the  arms 

of  a  lever,  given  in  §  168.     In  Fig.  41,  we 

Aave  represented  a  very  simple  kind  of 

bent  lever,  which  is  sufficiently  explained 

by  the  engraving.     In  Fig.  42,  we  have  a 

representation  of  a  curved  rod  lever,  WP',  at  the  ends  of 

which  two  forces, 
not  parallel,  are 
acting.  Our  def- 
inition of  the 
arms  of  the  lever, 
already  learned, 
removes  every  dif 

ficulty  arising  from  the  form  of  the  lever,  or  the  direction 

in  which  the  forces  act.    The  arms  are  not  FP'  anci 

but  FP  and  FW, 


FIG.  41. 


FIG.  42. 


92  THE  LEVER. 

174.   Load    between   Two    Supports.—//  a 

beam  rest  on  two  supports,  and  carry  a  load  be- 
tween them,  the  beam  may  be  considered  a  lever 
of  the  second  class.  The  part  carried  by  either  support 
may  be  found  by  considering  it  as  the  power,  and  the. 
other  support  as  the  fulcrum.  (Fig.  43.) 


FIG.  43. 


175.  The  Balance. — The  balance  is  essentially 
a  lever  of  the  first  class,  having  equal  arms.  Its 
use  is  to  determine  the  relative  weights  of  bodies.  Its 
action  depends  upon  the  equality  of  moments  explained  in 
§  171  and  §  172.  The  lever  itself  is  called  the  beam. 
From  the  ends  of  the  beam  are  suspended  two  pans,  one 
to  carry  the  weights  used,  the  other  to  carry  the  article  to 
be  weighed.  An  index  needle,  or  pointer,  is  often  attached 
to  the  beam,  and  indicates  equilibrium,  by  pointing  to  the 
zero  of  a  graduated  scale,  carried  by  a  fixed  support. 

(a.)  That  the  balance  may  be  accurate,  the  arms  must  be  of  the  same 
length.  To  make  these  arms  exactly  equal  is  far  from  an  easy  task. 
That  the  balance  may  be  delicate,  it  must  turn  upon  its  axis  with 


THE  LEVEti. 


little  friction,  the  axis  of  support  must  be  a  very  little  above  "the 
centre  of  gravity,  the  arms  must  be  of  considerable  length,  and  the 
beam  must  be 
light.  Balances  are 
made  so  delicate 
that  they  may  be 
turned  by  less  than 
a  thousandth  of  a 
grain.  The  sup- 
porting edge  of  the 
axis  is  made  very 
sharp  and  hard, 
and  rests  upon  two 
supports,  general- 
ly made  of  agate 
or  polished  steel. 
A  really  good  bal- 
ance is  an  expen- 
sive piece  of  appa- 
ratus. 


FIG.  44. 


176.  False  Balances. — False  balances  (Levers  of 
the  first  kind  with  unequal  arms)  are  sometimes 
used  ~by  dishonest  dealers.    When  buying,  they  place 
the  goods  on  the  shorter  arm ;  when  selling,  on  the  longer. 
The  cheat  may  be  exposed  by  changing  the  goods  and 
weights  to  the  opposite  sides  of  the  balance.     The  true 
weight  may  be  found  by  weighing  the  article  first  on  one 
side  and  then  on  the  other,  and  taking  the  geometrical 
mean  of  the  two  false  weights ;   that  is,  by  finding  the 
square-root  of  the  product  of  the  two  false  weights. 

177.  Double  Weighing1. — In  another  way  the  true 
weight  of  a  body  may  be  found  with  a  false  balance.     The 
article  to  be  weighed  is  placed  in  one  pan,  and  a  counter- 
weight, as  "of  shot  or  sand,  placed  in  the  other  pan  until 
equilibrium  is  produced.    The  article  is  then  removed, 
and  known  weights  placed  in  the  pan  until  equilibrium  is 


94 


THE  LEVER. 


again  produced.  The  sum  of  these  weights  will  be  the 
true  weight  of  the  given  article. 

178.  Compound  Lever.— Sometimes  it  is  not  con* 

venient  to  use  a  lever  sufficiently  long  to  make  a  giver 
power  support  a  given  weight.  A  combination  of  levers 
called  a  compound  lever  may  then  be  used.  Hay-scales 
may  be  mentioned  as  a  familiar  illustration  of  the  com- 
pound lever.  In  this  case  we  have  the  following : 

Statical  Law. — The  contin- 
ued product  of  the  power  and 
the  lengths  of  the  alternate 
arms,  beginning  ivith  the 
power-arm,  equals  the  contin- 
ued product  of  the  weight 
and  the  lengths  of  the  alter- 
nate arms  beginning  with  the 
weight-arm. 


.A 


xms 


x? 


d 

•) — f? 


FIG.  45. 


EXERCISES. 


No. 

!i 

§1 
P 

'k 

I 

No. 

IB 

£« 

Us 

P 

0) 

1 

f 

* 

Lever. 

Length. 

Class. 
? 

I 

4ft. 

2ft. 

50  Ibs. 

? 

11 

5ft. 

? 

SOlbs. 

25  Ibs. 

10ft. 

2 

3ft. 

9ft. 

? 

75  Ibs. 

12 

? 

9 

15  oz. 

45  oz. 

12  in. 

2 

3 

10ft. 

4ft. 

141bs. 

? 

13 

? 

50cm. 

IKg. 

4  Kg. 

? 

2 

4 

60  in. 

? 

21bs. 

SOlbs. 

14 

16.1cm. 

? 

12  oz. 

2oz. 

? 

3 

6 

? 

18cm. 

27  Kg. 

9  Kg. 

15 

3ft. 

5ft. 

10  Ibs. 

? 

? 

1 

6 

14ft. 

? 

45  oz. 

63  oz. 

16 

39.37  in. 

50cm. 

? 

20  Kg. 

? 

1 

7 

40cm. 

56cm. 

21  g. 

? 

17 

? 

16ft. 

14  Ibs. 

3i  Ibs. 

16ft. 

? 

8 

18  in. 

21  in. 

? 

24  oz. 

18 

? 

2ft. 

30  Ibs. 

? 

10ft. 

1 

9 

26cm. 

? 

iii)g. 

13  Dg. 

19 

? 

2ft. 

SOlbe. 

? 

10ft. 

2 

10 

? 

1ft. 

SOlbs. 

2500  Ibs. 

20 

2ft. 

? 

30  Ibs. 

? 

10ft. 

3 

Note  to  the  Pupil. — If  any  of  these  problems  be  obscure  to  you. 
remember  that  it  will  pay  to  draw  an  accurate  figure  or  diagram  of 
the  machine  representing  the  several  powers  and  weights  in  position. 
Bee  Fig.  40. 


TtfE  LEVER.  95 

21.  If  a  power  of  50  pounds  acting  upon  any  kind  of  machine, 
move  15  feet,  (a)  how  far  can  it  move  a  weight  of  250  pounds  1 
(&.)  How  great  a  load  can  it  move  75  feet? 

22.  If  a  power  of  100  pounds  acting  upon  a  machine,  moves  with 
a  velocity  of  10  feet  per  second,  (a)  to  how  great  a  load  can  it 
give  a  velocity  125  feet  per  second  ?    (&.)  With  what  velocity  can  it 
move  a  load  of  200  pounds? 

23.  A  lever  is  10  feet  long  ;  F  in  the  middle ;   a  power  of  50 
pounds  is  applied  at  one  end  ;   (a)  how  great  a  load  at  the  other  end 
can  it  support?    (&.)  How  great  a  load  can  it  lift  ? 

Ans.  to  (&.) :  Anything  less  than  50  Ibs. 

24.  The  power-arm  of  a  lever  is  10  feet ;  the  weight-arm  is  5  feet. 
(a.)  How  long  will  the  lever  be  if  it  is  of  the  first  class?    (&.)  If  it 
is  of  the  second ?     (c.)  If  it  is  of  the  third  class? 

25.  A  bar  12  feet  long  is  to  be  used  as  a  lever,  keeping  the  weight 
3  feet  from  the  fulcrum,     (a.)  What  class  or  classes  of  levers  may 
it  represent  ?    (&.)  What  weight  can  a  power  of  10  pounds  support 
in  each  case? 

26.  Length  of  lever  =  10  feet.    Four  feet  from  the  fulcrum  and  at 
the  end  of  that  arm  is  a  weight  of  40  pounds  ;  two  feet  from  the 
fulcrum  on  the  same  side,  is  a  weight  of  1,000  pounds.    What  force 
at  the  other  end  will  counterbalance  both  weights  ?  Ans.  360  Ib. 

27.  At  the  opposite  ends  of  a  lever  20  feet  long,  two  forces  are 
acting  whose  sum  =  1,200  pounds.     The  lengths  of  the  lever  arms 
are  as  2  to  3  ;  what  are  the  two  forces  when  the  lever  is  in  equi- 
librium ? 

28.  Length  of  lever  =  8  feet,  F  in  the  centre.      A  force  of  10 
pounds  acts  at  one  end,  one  foot  from  it  another  of  100  pounds. 
Three  feet  from  the  other  end  is  a  force  of  100  pounds.     Direction 
of  all  forces,  downward.     Where  must  a  downward  force  of  80 
pounds  be  applied  to  balance  the  lever  ?  Ans.  3  ft.  from  F. 

29.  Length  of  lever  ab  =  6£  feet  ;    fulcrum  at  c ;  a  downward 
force  of  60  pounds  acts  at  a  ;  one  of  75  pounds  at  a  point  d  between 
a  and  c,  2|  feet  from  the  fulcrum  ;  required  the  amount  of  equili- 
brating force  acting  at  b,  the  distance  between  b  and  c  being  f  feet. 

30.  On  a  lever  ab,  a  downward  force  of  40  pounds  acts  at  a,  10 
feet  from  fulcrum  c ;  on  same  side  and  6|  feet  from  c,  an  upward 
force,  d,  acts,  amounting  to  56  pounds ;   distance  be  =  3  feet  :    a 
downward  force  of  96  pounds  acts  at  b.    (a.)  Where  must  a  fourth 
force  of  28  pounds  be  applied  to  balance  the  lever,  and  (&)  what 
direction  must  it  have  ? 

31.  A  beam  18  feet  long  is  supported  at  both  ends  ;  a  weight 
of  1  ton  is  suspended  3  feet  from  one  end,  and  a  weight  of  14  cwt. 


96  THE  LEVER. 

8  feet  from  the  other  end.     Give  the  pressure  on  each  point  of  sup- 
port. Ans.  2288|  Ib.  at  one  end. 

32.  Length  of  lever  =  3  feet ;  where  must  the  fulcrum  be  placed 
so  that  a  weight  of  200  Ibs.  at  one  end  shall  be  balanced  by  40  Ibs. 
at  the  other  end  ? 

33.  In  one  pan  of  a  false  balance,  a  roll  of  butter  weighs  1  Ib. 

9  oz. ;  in  the  other,  2  Ibs.  4  oz.    Find  the  true  weight. 

34.  A  and  B  at  opposite  ends  of  a  bar  6  ft.  long  carry  a  weight 
of  800  Ibs.  suspended  between  them.     A's  strength  being  twice  as 
great  as  B's,  where  should  the  weight  be  hung  ? 

35.  A  and  B  carry  a  quarter  of  beef  weighing  450  pounds  on  a 
rod  between  them.     A's  strength  is  1£  that  of  B's ;  the  rod  is  8 
feet  long  ;  where  should  the  beef  be  suspended  ? 

36.  Length  of  lever  =  16  feet ;  weight  at  one  end,  100  pounds  : 
what  power  applied  at  other  end,  3|  feet  from  the  fulcrum,  is  re- 
quired to  move  the  weight  ? 

37.  A  power  of  50  Ibs.  acts  upon  the  long  arm  of  a  lever  of  the 
first  class  ;  the  arms  of  this  lever  are  5  and  40  inches  respectively. 
The  other  end  acts  upon  the  long  arm  of  a  lever  of  the  second 
class  ;  the  arms  of  this  lever  are  6  and  33  inches  respectively,     (a.) 
Figure  the  machine.     (&.)  Find  the  weight  that  may  be  thus  sup- 
ported,    (c.)  What  power  will  support  a  weight  of  4,400  kilograms  ? 

Recapitulation.— To  be  amplified  by  the  pupil  for 
review. 

DEFINITION. 

RELATION  TO  ENERGY. 

USE. 

GENERAL  LAWS. 


W 


DEFINITION. 
ARMS. 

STATIC  LAWS. 

( True. 
,  i.  BALANCE.-?  r>au/>fo 

THE  LEVER.    .    .     1  '  * False •* 

CLASSES.  T 

2.    LOAD    BETWEEN  TWO  SUPPORTS. 

BENT. 
COMPOUND. 

MOMENTS  OF  FORCES. 


THE    WHEEL    AND    AXLE. 


97 


ECTION  H. 


THE   WHEEL  AND   AXLE   AND   WHEEL-WORK. 

179.  The  Wheel  and  Axle.— The  wheel  and 
axle  consists  of  a  wheel  united  to  a  cylinder  in 
such  a  way  that  they  may  revolve  together  about 
a  common  axis.  It  is  a  modified  lever  of  the  first 
or  second  class. 

ISO.  Advantages  of  the  Wheel  and  Axle. — 

The  ordinary  range  of  action  of  a  lever  of  the  first  clasc 

is  very  small.     In  order  to  raise  the 

load  higher  than  the  vertical  distance 

through  which  the  weight  end  of  the 

lever  passes,  it  is  necessary  to  support 

the  load  and  re-adjust  the  fulcrum. 

This  occasions  an  intermittent  action 

and  loss  of  time,  difficulties  which  are 

obviated  by  using  the  wheel  and  axle. 


FIG.  46. 


181.  A  Modified  Lever. — Considered  as  a  lever 
of  the  first  class,  the  fulcrum  is  at 
the  common  axis,  while  the  arms  of 
the  lever  are  the  radii  of  the  wheel 
and  of  the  axle.  If  a  c,  the  radius 
of  the  wheel,  be  used  as  the  power- 
arm,  velocity  or  time  is  exchanged 
for  intensity  of  power.  This  is  the 
usual  arrangement.  If  be,  the  radius 
FIG.  47.  of  the  axle,  be  used  as  the  power- 


98  T&E   WHEEL  AND  AXLE. 

arm,  there  will  be  an  exchange  of  intensity  of  power  for 
velocity  or  time.  In  treating  of  the  wheel  and  axle,  unless 
otherwise  specified,  reference  is  made  to  the  former  or  usual 
arrangement. 

182.   Formulas  for  Wheel  and  Axle.— The 
law  and  formula  for  the  lever  apply  here : 

P  :   W  : :  WF  :  PF,        or,    P  :  W  : :  r  :  R, 

the  radii  of  the  wheel  and  of  the  axle  respectively  being 
represented  by  R  and  r.  But  it  is  a  geometrical  truth 
that  in  any  two  circles,  the  ratio  of  their  radii  is  the  same 
as  the  ratio  of  their  diameters  or  circumferences.  Hence 
=ji  these  ratios  may  be  substituted  for 

Jj-ij mmmr~~\n^  tne  ra^°  Between  ^ne  ra^"  °f  the 

wheel  and  axle ;  or, 

P  :   W  ::   r  :  R. 
P  :   W  ::  d:  D. 


J 

FIG.  48.  P  :   W  : :  c  :  C. 

183.  Law   of  Wheel   and  Axle. — The  power 
multiplied    by    the    radius,    diameter   or    circum- 
ference of  the  wheel  equals  the  weight  multiplied 
by  the  corresponding  dimension  of  the  axle. 

Note. — If  the  radius  of  the  axle  be  made  the  power-arm,  the  for- 
mulas will  be  as  follows  : 

P:W::WF:PF,        or,    P  :  W  ::  D  :  d. 

184.  Various  Forms  of  Wheel  and  Axle.— 

The  wheel  and  axle  appears  in  various  forms.  It  is  not 
necessary  that  an  entire  wheel  be  present,  a  single  spoke 
or  radius  being  sufficient  for  the  application  of  the  power, 


WHEEL   AND  A%LE. 


99 


FIG.  49. 


as  in  the  case  of  the  windlass  (Fig.  48)  or  capstan  (Fig.  49), 

In  ill  such  cases,  the  radius  being 

given,  the  diameter  or  circumference 

of  the  wheel  may  be  easily  computed. 

In  one  of  the  most  common  forms, 

the  power  is  applied  by  means  of  a 

rope  wound  around  the  circumference 

of  the  wheel.      When   this  rope  is 

unwound  by  the  action  of  the  power,  another  rope  is  wound 

up  by  the  axle,  and  the  weight  thus  raised. 

185.  Wheel-work.— Another  method  of  securing 

a  great  difference  in  the  in- 
tensities of  balancing  forces, 
is  to  use  a  combination  of 
wheels  and  axles  of  moder- 
ate size.  Such  a  combination 
constitutes  a  train.  The  wheel 
that  imparts  the  motion  is 
called  the  driver  ;  that  which 
receives  it,  the  follower.  An 
axle  with  teeth  upon  it  is 
called  a  pinion.  The  teeth  or 
cogs  of  a  pinion  are  called  leaves. 

186.  Law  of  Wheel-work,— A  train  of  wheel- 
work  is  clearly  analogous  to  a  compound  lever;  the  statical 
law,  given  in  §  178,  may  be  adapted  to  our  present  pur- 
poses as  follows :     The  continued  product  of  the  power 
and  the  radii  of  the  wheels  equals  the  continued 
product  of  the  weight  and  the  radii  of  the  axles. 

187.  Another     Law    of    Wheel-work.— By 

examination  of  Fig.  50,  it  will  be  seen  that  while  the  axle 


FIG.  50. 


100  WHEEL-WORK. 

d  revolves  once,  the  wheel  and  pinion  c  will  revolve  as 
many  times  as  the  number  of  leaves  borne  by  c  is  con- 
tained times  in  the  number  of  teeth  borne  by  /.  In  like 
manner,  while  the  wheel  c  revolves  once,  the  wheel  and 
pinion  ft  will  revolve  as  many  times  as  the  number  of  leaves 
borne  by  I  is  contained  times  in  the  number  of  teeth 
borne  by  c.  By  combination  of  these  results,  we  see  that 
while  d  revolves  once,  b  will  have  as  many  revolutions  as 
the  product  of  the  number  of  leaves  is  contained  times  in 
the  product  of  the  number  of  teeth.  From  this  it  follows 
that  the  ratio  between,  the  continued  product  of  the  cir- 
cumference (diameter  or  radius)  of  d  into  the  number  of 
leaves  on  the  several  pinions  and  the  continued  product  of 
the  corresponding  dimension  of  b  into  the  number  of  teeth 
on  the  several  wheels  will  be  the  ratio  between  the  dis- 
tances or  velocities  of  W  and  P,  and  therefore  the  ratio 
between  the  intensities  of  balancing  weights  or  forces. 

In  short,  the  continued  product  of  the  power,  the  cir- 
cumference of  a  and  the  number  of  teeth  on  c  and  f 
equals  the  continued  product  of  the  weight,  the  circum- 
ference of  d  and  the  number  of  leaves  on  the  pinions  c 
and  I. 

188.  Example. — Suppose  the  circumferences   of  a 
and  d  to  be  60  mm.  and  15  mm.  respectively  ;  that  ft  has  9 
leaves ;    c  has  36  teeth  and   13  leaves ;  /  has  40  teeth. 

Then  will 

P  x  60  x  36  x  40  =  W  x  15  x  13  x  9. 

189.  Ways   of  Connecting  Wheels.— Wheels 
may  be  connected  in  three  ways : 

(1.)  By  the  friction  of  their  circumferences. 
(2.)  By  bands  or  belts. 


WHEEL-  WORK. 


101 


(3.)  By  teeth  or  cogs. 

The  third  of  these  methods  has  been  already  considered, 

190.  Uses  of  the  First  Two  Ways.— The  first 
method  is  used  where  no  great  resistance  is  to  be  overcome, 
but  where  evenness  of  motion  and  freedom  from  noise  are 
chiefly  desired.     It  is  illustrated  in  some  sewing-machineSo 
The  second  method  is  used  when  the  follower  is  to  be  at 
some  distance  from  the  driver.     The  friction  of  the  belt 
upon  the  wheels  must  be  greater  than  the  resistance  to  be 
overcome.    It  is  illustrated  in  most  sewing-machines,  and 
in  the  spinning-wheel. 

191.  Relation   of    Power   to   Weight   De- 
termined.— The  follower  will  revolve  as  many  times 
as  fast  as  the  driver,  as  its  circumference   is  contained 
times  in  that  of  the  driver.     The  problem  of  finding  the 
distances  passed  over  in  a  given  time  by  the  power  and 
weight,  and  thence  the  relative  intensities  of  the  power 
and  the  weight,  thus  becomes  an  easy  one. 

EXERCISES. — The  Wheel  and  Axle. 

Reinark. — The  circumference  of  a  circle  is  3.1416  times  greatel 
than  its  diameter. 


*t 

? 

1 

2 
3 
4 
5 
6 
7 
8 
9 
10 
11 

Power. 

I 

DIMENSIONS. 

R 

D 

0 

r 

d 

c 

25  Ibs. 
? 
231bs. 
9  Kg. 
1341  Kg. 
195  Ibs. 
? 
3  Ibs. 
2  Ibs. 
49  Ibs. 
13  oz. 

? 
750  Kg. 
230  Ibs. 
153  Kg. 
? 
? 
80  Kg. 
48  Ibs. 
40  Ibs. 
? 
? 

f 

20  <"t. 

4ft. 
50cm. 
? 
17cm. 

15  in. 

12.50  m. 



? 
? 



15ft. 

? 
628.32  cm. 
25  in. 

...... 

20cm. 

1m. 
3dm. 

16  in. 



? 
? 

? 
? 
7  in. 

10cm. 

16  in. 

78.74  in. 

102 


WHEEL-  WORK. 


12.  The  pilot-wheel  of  a  boat  is  3  feet  in  diameter  ;  the  axle,  6 
inches.     The  resistance  of  the  rudder  is  180  pounds.     What  power 
applied  to  the  wheel  will  move  the  rudder? 

13.  Four  men  are  hoisting  an  anchor  of  1  ton  weight ;  the  barrel 
of  the  capstan  is  8  inches  in  diameter.     The  circle  described  by  the 
handspikes  is  C  feet  8  inches  in  diameter.      How  great  a  pressure 
must  each  of  the  men  exert  ? 

14.  With  a  capstan,  four  men  are  raising  a  1000  pound  anchor. 
The  barrel  of  the  capstan  is  a  foot  in  diameter ;  the  handspikes 
used  are  5  feet  long  ;    friction  equals  10  per  cent  of  the  weight. 
How  much  force  must  each  man  exert  to  raise  the  anchor  ? 

15.  The  circumference  of  a  wheel  is  8  ft.;  that  of  its  axle,  16 
inches.     The  weight,  including  friction,  is  85  .pounds  ;  how  great  a 
power  will  be  required  to  raise  it  ? 

16.  A  power  of  70  pounds,  on  a  wheel  whose  diameter  is  10  feet, 
balances  300  pounds  on  the  axle.     Give  the  diameter  of  the  axle. 

17.  An  axle  10  inches  in  diameter,  fitted  with  a  winch  18  inches 
long,  is  used  to  draw  water  from  a  well.    («.)  How  great  a  power  will 
it  require  to  raise  a  cubic  foot  of  water  which  weighs  62 \  Ibs.  ?    (b.) 
How  much  to  raise  20  litres  of  water  ? 

18.  A  capstan  whose  barrel  has  a  diameter  of  14  inches  is  worked 
Dy  two  handspikes,  each  7  feet  long.     At  the  end  of  each  handspike 
a  man  pushes  with  a  force  of  30  pounds  ;    2  feet  from  the  end  of 
each  handspike,  a  man  pushes  with  a  force  of  40  pounds  ;  required 
the  effect  produced  by  the  four  men. 

19.  How  long  will  it  take  a  horse  working  at  the  end  of  a  bar  7 
feet  long,  the  other  end  being  in  a  capstan  which  has  a  barrel  of  14 
inches  in  diameter,  to  pull  a  house  through  5  miles  of  streets,  if  the 
horse  walk  at  the  rate  of  2|  miles  an  hour  ? 

Recapitulation. — To  be  amplified  by  the  pupil  for 


review. 


WHEEL 
AND    AXLE. 


DEFINITIONS. 

ADVANTAGES. 

RELATION  TO  THE  LEVER. 

FORMULAS  AND  LAWS. 

FORMS. 


WHEEL    WORK. 


DRIVER. 
FOLLOWER. 
LAWS. 
CONNECTIONS. 


MODES 
USES. 
RELATION  OF  P  TO  W 


THE    PULLEY. 


103 


ECTfON  III, 


PULLEY  AND   THE    INCLINED    PLANE. 

192.  What  is  a  Pulley?—^  pulley  consists  of 
a  wheel  turning  upon  an  axis  and  having  a  cord 
passing  over  its  grooved  circumference.     The  frame 
supporting  the  axis  of  the  wheel  is  called  the  block. 

193.  A  Fixed    Pulley.— The  advantages  arising 
from  the  use  of  a  pulley  depend  upon  the  uniform  tension 
of  the  cord.     If  a  cord  be  passed  over  a 

pulley  fixed  to  the  ceiling,  a  weight  being 
at  one  end  and  the  hand  applied  at  the 
other,  the  tension  of  the  cord  will  be  uni- 
form, and  the  hand  will  have  to  exert  a 
force  equal  to  the  weight  of  the  load.  If 
the  weight  be  moved,  the  hand  and  weight 
will  move  equal  distances.  It  is  evident, 
ihen,  that  the  fixed  pulley  affords  no 
increase  of  power,  but  only  change 
of  direction. 

194.  A  Movable  Pulley.— If  one 

end  of  the  cord  be  fastened  to  the  ceil- 
mg,  the  load  suspended  from  the  pulley, 
and  the  other  end  of  the  cord  drawn  up 
by  the  hand,  it  will  be  evident,  from  the 
equal  tension  of  the  cord,  that  the  fixed 
support  carries  half  the  load  and  the  hand 
the  other  half.  It  is  also  evident  that  to 
raise  the  weight  one  foot  the  hand  must 
pull  up  two  feet  of  the  cord ;  that  is  to  FIG-  52- 


FIG.  51. 


104 


THE  PULLET. 


say,  each  section  of  the  cord  carrying  the  weight  must  be 
shortened  one  foot.  Thus  the  hand,  by  lifting  50  pounds 
two  feet,  is  able  to  raise  100  pounds  one  foot.  It  is  to  be 
noticed  that  we  have  here  no  creation  or  increase  of 
energy,  working  power,  but  that  we  do 
secure  an  important  transformation  of 
velocity  into  intensity. 

195.  A  Combination  of  Pul- 
leys.— By  the  use  of  several  fixed  and 
movable  pulleys  in  blocks,  the  number 
of  parts  of  the  cord  supporting  the  mov- 
able block  may  be  increased  at  pleasure. 
In  all  such  cases,  the  tension  of  the  cord 
will  be  uniform,  and  the  part  of  the  cord 
to  which  the  power  is  applied,  will  carry 
only  a  part  of  the  load.  The  value 
of  this  part  of  the  load  depends  upon 
the  number  of  sections  into  which  the 
movable  pulley  divides  the  cord. 

FIG.  53-  196.  Law   of   the   Pulley.— 

With  a  pulley  having  a  contin- 
uous cord,  a  given  power  will  support  a 
weight  as  many  times  as  great  as  itself  as 
there  are  parts  of  the  cord  supporting  the 
•movable  block. 

197.  Concerning:  the  Number  of 
Parts  of  the  Corel.— By  observing  the  sev- 
eral figures  of  pulleys  in  this  section,  it  will  be 
seen  that  when  the  fixed  end  of  the  cord  is  at- 
tached to  the  fixed  block,  the  number  of  parts  ol 
FIG.  54.  the  cord  supporting  the  weight  is  twice  the  num- 


THE  INCLINED  PLANE.  105 

her  of  movable  pulleys  used ;  that  when  the  fixed  end  of 
the  cord  is  attached  to  tt.a  movable  block  the  number  of 
parts  of  the  cord  is  one  more  than  twice  the  number  of 
movable  pulleys  used. 

198.  What  is  an  Inclined  Plane?— The  in- 
clined plane  is  a  smooth,  hard,  inflexible  surface 
inclined  so  as  to  make  an  oblique  angle  with  the 
direction  of  the  force  to  be  overcome.    In  most  cases  it 
is  a  plane  surface  inclined  to  the  horizon  at  an  acute  angle, 
and  is  used  to  aid  in  the  performance  of  work  against  the 
force  of  gravity. 

199.  Resolution  of  the  Force  of  Gravity.— 

When  a  weight  is  placed  upon  an  inclined  plane,  the  force 
of  gravity  tends  to  draw  it  vertically  downward.  This 
force  may  be  resolved  into  two  forces  (§  91),  one  acting  per- 
pendicularly to  the  plane,  producing  pressure  completely 
resisted  by  the  plane,  the  other  component  acting  opposite 
to  the  direction  of  the  power  which  it  is  to  counterbalance. 
The  first  component  shows  how  much  pressure  is  exerted 
upon  the  plane ;  the  other  shows  what  force  must  be 
exerted  to  maintain  equilibrium.  The  value  of  the  second 
component  will,  plainly,  vary  with  the  direction  of  the 
power. 

200.  Three   Cases. — In  the  use  of  an  inclined  plane,  three 
cases  may  arise : 

(1.)  Where  the  power  acts  in  a  direction  parallel  to  the  length  of 
the  plane. 

(2.)  Where  the  power  acts  in  a  direction  parallel  to  the  base  of  the 
plane  (generally  horizontal). 

(3. )  Where  the  power  acts  in  a  direction  parallel  to  neither  the 
length  nor  the  base  of  the  plane. 

20 1.  The  First  Case.— In  the  accompanying   figure,  let 


106 


THE  INCLINED  PLANE. 


\ 


]St 


c 
FIG.  55. 


LM  represent  a  plane  inclined  to  the  horizontal  line  LN.  Let  A 
represent  a  ball  weighing  20  Kg.  The 
problem  is  to  find  what  force  acting  in  the 
direction  LM  will  hold  it  in  equilibrium. 
The  weight  of  the  body  A  is  a  downward 
force  of  20  Kg.,  which  may  be  graphically 
represented  (§  81)  by  the  vertical  line  AC, 
20  mm.  in  length.  Any  other  convenient 
unit  of  length  might  be  used,  but  the 
scale  of  1  mm.  to  the  Kg.  being  adopted, 
it  must  be  maintained  throughout  the 
problem.  The  force  represented  by  AC 
is  resolved  into  two  components  repre- 
sented by  AD,  perpendicular  to  LM,  and  by  AB,  parallel  to  it.  The 
former  component  measures  the  pressure  to  be  resisted  by  the  plane  ; 
the  latter  component  measures  the  force  with  which  the  ball  is 
drawn  towards  L.  This  second  component  is  to  be  balanced  by  the 
equal  and  opposite  force  AB',  the  equilibrant  of  AB.  It  may  be 
proved  geometrically  that 

AB  :  AC  : :  MN  :  ML.    (Olney's  Geometry,  Art.  341.) 
Careful  construction  and  measurement  will  give  the  same  result. 
But  AB,  or  rather  its  equal  AB',  represents  the  power  ;   AG  repre- 
sents the  weight  ;  MN  represents  the  height ;  and  ML,  the  length 
of  the  plane.     Therefore, 

P  :  W  ::h:l,      or,      P  =  the  |  part  of  W. 

2O2.  Law  for  the  First  Case.— In  the  figure 
above,  ML  is  twice  the  length  of  MN,  and  AC  is  twice  the 
length  of  AB  or  AB'.  This  indi- 
cates that  a  force  of  10  Kg.  acting  in 
the  direction  LM  would  hold  the 
ball  in  equilibrium.  This  result  may 
be  easily  verified  by  experiment. 
We  may  therefore  establish  the  fol- 


20 Kg. 


FIG.  56. 


10  Kg.  < 


lowing  law :  When  a  given  power 
acts  parallel  to  the  plane,  it  will 
support  a  weight  as  many  times  as  great  as  itself  as 
the  length  of  the  plane  is  times  as  great  as  its  verti- 
cal height. 


THE  INCLINED  PLANE 


107 


203.  Law  for  the  Second  Case. — By  resolving 
the  force  of  gravity,  or  by  experi- 
ment,  the  following  law  may  be 

established :  When  a  given  power 
acts  parallel  to  the  base,  it  mill 
support  a  weight  as  many 
times  as  great  as  itself  as  the 
horizontal  base  of  the  plane  is 
times  as  great  as  its  vertical 
height. 

204.  The    Third    Case.— For  the  third  case,  the  power 
acting  in  a  direction  parallel  to  neither  the  length  nor  the  base  of 
the  plane,  no  law  can  be  given.     The  ratio  of  the  power  to  the 
weight  may  be  determined  by  resolving  the  force  of  gravity,  as 
above  explained,  the  construction  and  measurement  being  carefully 
done. 

EXERCISES. 

Remark. — The  first  problem  may  be  read  : 

(a.)  In  a  system  of  pulleys,  the  weight  being  supported  by  two 
sections  of  the  cord,  a  power  of  25  Ibs.  will  support  what  weight  ? 

(6.)  In  an  inclined  plane,  the  power  acting  in  the  direction  of  the 
length,  the  height  being  3  ft.,  what  must  be  the  length  that  a  power 
of  25  Ibs.  may  support  the  same  weight  as  determined  in  (a.)? 


PULLET. 

lN< 

3LINED  I 

JLANE. 

No. 

POWER. 

WEIGHT. 

Cords. 

Height. 

Length. 

Base. 

Case. 

1 

25  Ibs 

? 

2 

3  ft 

? 

1 

2 

13  Ke- 

78  Kff 

? 

? 

12  m 

1 

3 

12  OZ5 

? 

8 

? 

2  ft. 

2 

4 

250  a- 

2  Kg- 

? 

1  dm 

? 

1 

5 
3 

? 
15  cwt 

«  "-&• 
350  Ibs. 
3  T 

7 
7 

? 
4  rds 

? 

49ft. 

2 
I 

7 

20  a- 

1  He;. 

? 

? 

10m. 

2 

8 

•*v  g. 

500  Kg. 

? 

8 

? 

24m. 

1 

9 

7 

540  Ibs 

9 

39  37  in 

?m 

1 

10 

75  Ibs. 

100  Ibs. 

3yds. 

? 

? 

2 

108  THE  INCLINED  PLANE. 

11.  With  a  fixed  pulley,  what  power  will  support  a  weight  of  50 
pounds  ? 

12.  With  a  movable  pulley,  what  power  will  support  a  weight  of 
50  pounds  ? 

13.  What  is  the  greatest  effect  of  a  system  of  3  movable  and  4 
fixed  pulleys,  the  power  applied  being  75  pounds  ? 

14.  With  a  system  of  5  movable  pulleys,  one  end  of  the  rope 
being  attached  to  the  fixed  block,  what  power  will  raise  a  ton  1 

15.  If  in  the  system  mentioned  in  the  problem  above,  the  rope  be 
attached  to  the  movable  block,  what  power  will  raise  a  ton  ? 

16.  With  a  pulley  of  6  sheaves  in  each  block,  what  is  the  least 
power  that  will  support  a  weight  of  1,800  pounds,  allowing  \  for 
friction  ?    What  will  be  the  relative  velocities  of  P  and  W  ? 

17.  Figure  a  set  of  pulleys  by  which  a  power  of  50  pounds  will 
support  a  weight  of  250  pounds. 

18.  The  height  of  an  inclined  plane  is  one-fifth  its  horizontal 
base.    A  globe  weighing  250  Kg.  is  supported  in  place  by  a  force 
acting  at  an  angle  of  45°  with  the  base.    The  pressure  of  the  globe 
upon  the  plane  is  less  than  250  Kg.     By  construction  and  measure 
ment,  determine  the  intensity  of  the  supporting  force. 

19.  With  the  conditions  as  given  in  the  last  problem,  except  that 
Ihe  pressure  of  the  globe  upon  the  plane  is  more  than  250  Kg.,  de- 
termine the  intensity  of  the  supporting  force. 

20.  The  base  of  an  inclined  plane  is  10  feet ;  the  height  is  3  feet. 
What  force,  acting  parallel  to  the  base,  will  balance  a  weight  of 
JJtons? 

21.  An  incline  has  its  base  10  feet ;  its  height,  4  feet :  how  heavy  a 
ball  will  50  pounds  power  roll  up  f 

22.  How  great  a  power  will  be  required  to  support  a  ball  weighing 
40  pounds  on  an  inclined  plane  whose  length  is  8  times  its  height  ? 

23.  A  weight  of  800  pounds  rests  npon  an  inclined  plane  8  feet 
high,  being  held  in  equilibrium  by  a  force  of  25  pounds  acting 
parallel  to  the  base.     Find  the  length  of  the  plane. 

24.  A  load  of  2  tons  is  to  be  lifted  along  an  incline.    The  powej 
is  75  pounds  :  give  the  ratio  of  the  incline  which  may  be  used. 

25.  A  1500  pound  safe  is  to  be  raised  5  feet.    The  greatest  powei 
that  can  be  applied  is  250  pounds.     Give  the  dimensions  of  thf 
shortest  inclined  plane  that  can  be  used  for  that  purpose. 

Recalculation, — To  be  amplified  by  the  pupil  foi 
review. 


THE    WEDGE. 


109 


PULLEY. 


INCLINED 
PLANE. 


DEFINITION. 

r  FIXED. 

KINDS.  \  MOVABLE. 

[  COMBINATIONS. 

LAW. 

RELATION  between  the  number  of  pulleys  and  the 
number  of  parts  of  the  cord. 

f  DEFINITION. 
FORCE  OF  GRAVITY  I  FIRST  CASE-LAW- 

CAVITY  I  SECOND  CASE.-LAW. 
RESOLVED.         ]  THIRD  CASK 


ECTION    IV, 


J  \. 

THE  WEDGE,  SCREW,  COMPOUND  MACHINES,  AND 
FRICTION. 

2O5.  What  is  a  Wedge?— A  wedge  is  a  mov- 
able  inclined    plane    in 
which   the  power  gener- 
ally acts  parallel  to  the 


2O6.    Its    Use.  —  The 

wedge  is  used  for  moving 
great  weights  short  dis- 
tances. The  law  is  the  Fl&-  58. 
same  as  for  the  corresponding  inclined  plane.  A  common 
method  of  moving  bodies  is  to  place  two  similar  wedges, 
with  their  thin  ends  overlapping,  nnder  the  load. 
Simultaneous  blows  of  equal  force  are 
struck  upon  the  heads  of  the  wedges. 
In  this  case,  the  same  force  must  be 
used  upon  each  wedge  as  if  only  one 
FIG.  59.  were  used,  but  the  power  being  doubled 


110 


THE  SCREW. 


FIG.  60. 


and  the  weight  remaining  the  same,  the  distance  moved  in 
twice  as  great  as  when  only  one  wedge  is  used. 

207.  A  More  Common  Use. — A  more  com- 

mon, kind  of  wedge  is  that  of  two  in- 
clined planes  united  at  their  bases.  Such 
wedges  are  used  in  splitting  timher,  stone,  etc. 
The  power  is  given  in  repeated  blows  instead 
of  continued  pressure.  For  a  wedge  thus  used, 
no  definite  law  of  any  practical  value  can  be 
given,  further  than  that,  with  a  given  thick- 
ness, the  longer  the  wedge  the  greater  the  gain 
in  intensity  of  power. 

208.  What  is  a  Screw? — A  Screw  is  a  cylin* 
der,  generally  of  wood  F. 

or  metal,  with  a  spiral 
groove  or  ridge  winding 
ribout  its  circumference. 
The  spiral  ridge  is  called 
the  thread  of  the  screw. 
The  thread  works  in  a  nut, 
within  which  there  is  a 
corresponding  spiral  groove 
to  receive  the  thread. 

(a.)  The  power  is  used  to  turn  the  screw  within  a  fixed  nut,  or  to 
turn  the  nut  about  a  fixed  screw.  In  either  case,  a  lever  or  wheel 
Is  generally  used  to  aid  the  power.  Every  turn  of  the  screw  or  nut 
3ither  pushes  forward  the  screw  or  draws  back  the  nut  by  exactly 
fiie  distance  between  two  turns  of  tha  thread,  this  distance  being 
measured  in  the  direction  of  the  axis  c  f  the  screw.  The  weight  or 
resistance  at  W  is  moved  this  distance,  while  the  power  at  P  moves 
over  the  circumference  of  a  circle  whose  radius  is  PF.  The  differ- 
ence between  these  distances  is  generaU  T  very  great.  Hence  this 
machine  affords  great  intensity  of  power  vith  a  corresponding  loss 
of  velocity. 


FIG.  61. 


COMPOUND    MACHINES. 


Ill 


L 


209.  Law  of  the   Screw.— The  second  general 
law  of  machines  (§167,  [2])  may  be  adapted  to  our  present 
purpose  as  follows :   With  the  screw,  a  given  power  will 
support  a  weight  as  many  times  as  great  as  itself  as 
the  circumference  described  by  the  power  is  times  as 
great  as  the  distance  between  two  adjoining  turns 
of  the  thread. 

210.  The   Endless   Screw.— An  endless  screw 
is  one  whose  thread  acts  on  the  teeth  of  a  wheel. 
The  screw  has  a  rotary  but  no 

lengthwise  motion.  As  the  han- 
dle is  turned,  the  thread  catches 
the  teeth  and  turns  the  wheel. 
The  wheel  moves  one  tooth  for 
every  turn  of  the  handle.  Suc- 
cessive teeth  are  caught  as  others 
pass  out  of  reach.  A  continuous 
motion  is  thus  produced  ;  hence 
the  name  "endless  screw."  The 
figure  will  aid  in  the  application  of  the  second  general  law 
of  machines  to  determine  the  ratio  between  the  weight  and 
the  power. 

211.  Compound  Machines. — We  have  now  con- 
sidered each  of  the  six  traditional  simple  machines.     One 
of  these  may  be  made  to  act  upon  another  of  the  same 
kind,  as  in  the  case  of  the  compound  lever  or  wheel-work ; 
or  upon  another  of  a  different  kind,  as  in  the  case  of  the 
endless  screw.     When  any  two  or  more  of  these  machines 
are  combined,  the  effective  force  may  be  found  by  comput- 
ing the  effect  of  each  separately  and  then  compounding 
them  ;  or  by  finding  the  weight  that  the  given  power  wil) 


FIG.  62. 


112  FRICTION. 

support,  using  the  first  machine  alone,  considering  the 
result  as  a  new  power  acting  upon  the  second  machine, 
and  so  on. 

212.  What  is  Friction  ?— The  chief  impediment 
to  the  motion  of  machinery  arises  from  friction,  which  may 
be  defined  as  the  resistance  which  cu  moving   body 
meets  with  from  the  surface  on  which  it  moves. 

213.  The  Cause  of  Friction. — It  is  impossible, 
by  any  known  means,  to  produce  a  perfectly  smooth  sur- 
face.    Even  a  polished   surface  contains  minute  projec- 
tions which  fit  into  corresponding  depressions  on  the  cor- 
responding surface.     To  produce  motion  of  one  surface  on 
the  other,  these  projections  must  be  lifted  out,  bent  down, 
or  broken  off. 

214.  Eight   Facts  Concerning  Friction.— 
The  following  facts  have  been  determined  by  experiment, 
and  may  be  easily  illustrated  in  the  same  way : 

(1.)  Friction  is  greatest  at  the  beginning  of  motion. 
After  surfaces  have  been  in  contact  for  some  time, 
so  that  the  projections  of  one  have  had  opportunity 
to  sink  deeper  into  the  depressions  of  the  other,  the 
resistance  offered  by  friction  is  considerably  in- 
creased. Every  teamster  and  street-car  driver  is 
familiar  with  the  fact. 

(2.)  Friction  increases  with  the  roughness  of  the 
surfaces. 

(3.)  Friction  is  greater  between  soft  bodies  than 
hard  ones. 

(4.)  Friction  is  nearly  proportional  to  pressure, 
(a.)  Place  a  brick  upon  a  horizontal  board.     Around  it  fasten  one 

end  of  a  cord  and  pass  the  other  end  over  a  pulley  so  that  it  may 

hang  vertically.    Add  just  weights  enough  to  keep  the  brick  in 


FRICTION. 


113 


motion  after  it  is  started.  The  weights  measure  the  friction.  Place 
a  second  similar  brick  upon  the  first ;  the  moving  force  must  be 
doubled.  Place  another  similar  brick  upon  the  other  two  ;  the 
original  moving  force  must  be  tripled. 

(5.)  Friction  is  not  affected  by  extent  of  surface 
except  within  extreme  limits.  In  the  case  of 
the  brick  above  mentioned,  the  moving  force  will 
be  the  same  whether  the  brick  he  on  its  broad  face 
or  on  its  side. 

(6.)  Friction  is  greater  between  surfaces  of  the 
same  material  than  between  those  of  differ- 
ent kinds. 

(a.)  Bodies  of  the  same  material  have  the  same  molecular  struc- 
ture (§  10,  a).  Hence  their  little  projections  and  cavities  mutually 
fit  each  other  as  would  the  teeth  of  similar  saws.  A  very  little  re- 
flection will  show  that  the  element  of  similarity  in  molecular  struc- 
ture (just  as  with  the  saws)  is  very  important  in  determining  the 
amount  of  friction.  For  this  reason,  the  axles  of  railway  cars  being 
made  of  steel,  the  "  boxes  "  in  which  they  revolve  are  made  of  brass 
or  other  different  metal.  Hence  the  advantages  of  a  watch  "  full- 
jewelled,"  and  hence  the  swiftness  of  the  skillful  skater. 

(7.)  Rolling  friction  is  less  than  sliding  friction* 
(8.)  Friction  is  diminished  by  polishing  or  lubri- 
cating the  surfaces.    An  unequalled  example  of 
friction  reduced  to  its  minimum  is  in  the  case  of 
the  joints  of  animals. 

EXERCISES. — The  Screw. 


No. 

P. 

W. 

c. 

d. 

No. 

P. 

W. 

C. 

(I. 

1 

15  Ibs. 

? 

JO  in. 

iin. 

8 

? 

2500  Kg. 

2.5m. 

1  cm. 

2 

5  Kg. 

? 

8m. 

1  cm. 

9 

4  oz. 

6  Ibs. 

? 

7  in. 

3 

lib. 

? 

75  in. 

{in. 

10 

?lbs. 

7874  Ibs. 

1m. 

lin. 

1 

? 

480  Ibs. 

15  in. 

1-fe 

11 

3  Kg. 

aOOKg.i  20cm. 

? 

5 

20  Ibs. 

800  Ibs. 

? 

iin. 

12 

3  oz. 

864  oz. 

? 

1  in. 

6 

25  Ibs. 

? 

3ft. 

lin. 

13 

100  Ibs. 

? 

10ft. 

fin. 

7 

2  Ibs. 

192  Ibs. 

4ft. 

? 

14 

100  Ibs. 

? 

10ft. 

I  to. 

THE  SCREW. 


15.  A  book-binder  has  a  press;  the  threads  of  its  screw  are  \  in.  apart; 
the  nut  is  worked  by  a  lever  which  describes  a  circumference  of 
8  ft.     How  great  a  pressure  will  a  power  of  15  Ibs.  applied  at  the  end 
of  the  lever  produce,  the  loss  by  friction  being  equivalent  to  240  Ibs.  1 

16.  A  screw  has  11  threads  for  every  inch  in  length.     If  the 
lever  is  8  inches  long,  the  power,  50  pounds,  and  friction  is  $  of  the 
energy  used,  what  resistance  may  be  overcome  by  it  ? 

17.  A  screw  with  threads  1|  in.  apart  is  driven  by  a  lever  4|  ft. 
long  ;  what  is  the  ratio  of  the  power  to  the  weight  ?  (See  Appendix  A.  ) 

18.  How  great  a  pressure  will  be  exerted  by  a  power  of  15  Ibs. 
applied  to  a  screw  whose  head  is  one  inch  in  circumference  and 
whose  threads  are  %  inch  apart  ? 

19.  At  the  top  of  an  inclined  plane  which  rises  1  ft.  in  20  is  a  wheel 
and  axle.    Radius  of  wheel  =  2  *  ft.  ;  radius  of  axle  —  4|  in.    What  load 
may  be  lifted  by  a  boy  who  turns  the  wheel  with  a  f  orco  of  25  Ibs.  ? 

20.  The  crank  of  an  endless  screw  whose  threads  are  an  inch 
apart  describes  a  circuit  of  72  inches.     The  screw  acts  on  the 
toothed  edge  of  a  wheel  60  inches  in  circumference.     On  the  axle 
of  this  wheel,  which  is  10  inches  in  circumference,  is  wound  a  cord 
which  acts  upon  a  set  of  pulleys,  3  in  each  block.    The  effect  of  the 
pulleys  is  exerted  upon  the  wheel  of  a  wheel  and  axle.    The  diam- 
eters of  the  wheel  and  of  the  axle  are  4  ft.  and  6  inches  respec- 
tively.    What  weight  on  the  wheel  and  axle  may  be  lifted  by  a 
force  of  25  Ibs.  at  the  crank,  allowing  for  a  loss  of  1  by  friction  ? 

21.  An  endless  screw  which  is  turned  by  a  wheel  10  ft.  in  circum- 
ference acts  upon  a  wheel  having  81  teeth  ;  this  wheel  has  an  axle 
18  inches  in  circumference  ;  the  power  is  75  Ibs.     Find  the  value  of 
the  weight  that  may  be  suspended  from  the  axle. 

22.  In  moving  a  building  the  horse  is  attached  to  a  lever  7  feet 
long,  acting  on  a  capstan  barrel  11  inches  in  diameter  ;  on  the  barrel 
winds  a  rope  belonging  to  a  system  of  2  fixed  and  3  movable  pul- 
leys.    What  force  will  be  exerted  by  500  pounds  power,  allowing 
£  for  loss  by  friction  ? 

Recapitulation.  —  To  be  amplified  by  the  pupil  for 
review. 

%4/rrnnc          J  DEFINITION. 

WEDGE.       j  TWO  USES  AND  THE  LAW  FOR  EACH. 

(  DEFINITION. 
or»pc\*/         J  j  A.W 

{  ENDLESS  SCREW  ;  ITS  ADVANTAGES  ;  RELATION  OF  P  TO  W. 

COMPOUND  MACHINES;  RELATION  OF  p  TO  w. 

DEFINITION. 

FRICT.ON. 


REVIEW.  115 

REVIEW  QUESTIONS  AND  EXEKCISES. 

1.  («.)  What  is  a  machine?    (6.)  What  is  a  machine  good  forl 
c.)  State  the  general  laws  of  machines  and  (d)  illustrate  by  the 

pulley 

2.  («.)  What  are  the  arms  of  a  lever  ?    (&.)  What  is  meant  by  the 
moment  of  a  force  ?    (c.)  Illustrate  the  equality  of  moments  in  ma- 
chines by  the  wheel  and  axle. 

3.  (a.)  What  are  the  respective  advantages  to  be  gained  by  the 
several  classes  of  levers  ?    (b.)  Explain  the  advantage  gained  by  a 
claw  hammer  in  drawing  a  nail,    (c.)  What  is  meant  by  double 
weighing  ? 

4.  With  a  lever  of  given  length,  in  which  class  will  a  given 
power  yield  the  greatest  intensity  of  effect  ? 

5.  (a.)  To  what  kind  of  a  lever  is  ordinary  clock-work  analogous? 
(&.)  Show  why. 

6.  (a.)  Does  it  require  more 'work  to  lift  a  barrel  of  flour  into  a 
wagon  four  feet  high  than  to  place  it  there  by  rolling  it  up  a  plank 
12  feet  long  ?    (6.)  Show  why. 

7.  (a.)  Give  the  static  law  for  the  inclined  plane  when  the  power 
acts  parallel  to  the  plane.     (&.)  When  it  acts  parallel  to  the  horizon. 
(c.)  Figure  a  system  of  pulleys  by  means  of  which  a  weight  of  5 
pounds  will  support  a  weight  of  25  pounds. 

8.  (a.)  Figure  a  system  of  4  movable  pulleys  by  means  of  which 
a  weight  of  3  Ibs.  will  support  a  weight  of  27  Ibs.     (&.)  Deduce 
the  formula  for  the  screw  from  one  of  the  general  laws  of  machines. 

9.  (a.)  In  raising  a  boy  from  a  deep  well  by  means  of  a  common 
rope  and  pulley,  what  disadvantages  arise  from  friction  ?   (&.)  What 
immense  advantage  ? 

10.  (a.)  Explain  the  cause  of  friction.    (&.)  Why  is  friction  between 
iron  and  iron  greater  than  that  between  iron  and  brass? 

11.  (a.)  How  may  the  centre  of  gravity  of  a  ring  be  determined  ? 
(&,)  What  is  the  value  in  inches  of  the  metric  unit  of  length? 

,  12.  A  body  moving  with  an  energy  of  20  foot-pounds,  strikes  the 
end  of  the  arm  of  a  lever  of  the  first  class,  four  feet  from  the 
fulcrum,  (a.)  How  many  foot-pounds  will  be  exerted  by  the  other 
end  of  the  lever,  6  feet  from  the  fulcrum  ?  (&.)  How  far  would  it 
raise  a  weight  of  4  pounds  ? 

13.  Deduce  the  static  law  for  the  inclined  plane,  first  case,  by 
resolution  of  the  force  of  gravity. 

14.  (a.)  What  force  is  necessary  to  overturn  a  body  ?    (&.)  What 
difference  between  the  forces  producing  uniform  and  accelerated 
velocities  ?    (c.)  Show  that  the  screw  is  a  modified  ipclined  plane. 


IV. 


LIQUIDS. 


ECTION  I, 


HYDROSTATICS. 

215.  Incompressibility  of  Liquids. — Liquids 
are  nearly  incompressible.  A  pressure  of  15  pounds  to 
the  square  inch,  compresses  distilled  water  only  2  0  0*0  0  tf 
part  of  its  volume ;  it  compresses 
mercury  only  one-tenth  as  much. 
This  virtual  incompressibility  of 
liquids  is  of  the  highest  practical 
importance. 

216.  Transmission  of 
Pressure. — Fluids  can  trans- 
mit pressure  in  every  direc- 
tion, upward,  downward,  and 
sidewise  at  the  same  time. 

(a.)  This  property  of  liquids  may  be 
illustrated  by  the  apparatus  repre- 
sented in  Fig.  63.  The  globe  and 
cylinder  being  filled  with  water  and 
the  several  openings  in  the  globe 
FIG.  63.  closed  by  corks,  a  piston  is  pushed 


n  TD  R  OSTA  TICS. 


117 


FIG.  64. 


Jown  the  cylinder.  The  pressure  thus  received  and  transmitted  by 
the  confined  water  expels  the  cork  and  throws  a  jet  of  water  from 
each  aperture.  (See  Appendix  D.) 

(&.)  The  explanation  of  this  property  of  fluids  may  be  seen  by 
reference  to  Fig.  64,  representing  five  molecules  of  any  fluid.  If  a 
downward  pressure  be  applied  to  1,  it 
will  force  2  toward  the  right  and  3  tow- 
ard the  left,  thus  forming  lateral  pres- 
sure. When  thus  moved,  3  will  force  4 
upward  and  5  downward.  Owing  to  the 
freedom  with  which  the  molecules  move 
on  each  other,  there  is  no  loss  by  friction, 
and  the  downward  pressure  of  5,  the 
upward  pressure  of  4,  and  the  lateral 
pressure  of  2,  will  each  equal  the  pres- 
sure exerted  by  1.  It  makes  no  difference  with  the  fact,  whether 
the  pressure  exerted  by  1  was  the  result  of  its  own  weight  only, 
this  weight  together  with  the  weight  of  overlying  molecules,  o? 
both  of  these  with  still  additional  forces. 

217.  Pascal's    Law. — Pressure    exerted    any- 
where  upon    a    mass   of 

liquid  is 'transmitted  un- 
diminished  in  all  direc- 
tions, and  acts  with  the 
same  force  upon  all  equal 
surfaces  and  in  a  direc- 
tion at  right  angles  to 
those  surfaces. 

218.  An  Argument  from 

Pascal's  Law.— Fill  with  water 

a  vessel  of  any  shape,  having  in 

Its  sides  apertures  whose  areas  are 

respectively    as   1,  2  and    3,    each 

aperture  being  closed  with  a  piston. 

without  friction  and  the  water  to  have  no  weight ;  then  there  will 

be  no  motion.     Suppose  that  the  piston  whose  area  is  represented 

by  1  rests  upon  1000  molecules  of  the  water  ;  then  will  the  piston 

at  2  rest  upon  2000,  and  that  at  3  upon  3000  molecules  of  water. 

If  now  a  pressure  of  one  pound  be  applied  to  the  piston  at  1,  this 


FIG.  65. 
Suppose  the  pistons  to  move 


118 


FIG.  66. 


pressure  is  distributed  among  the  1000  molecules  upon  which  it 
presses.  Owing  to  this  freedom  of 
motion,  these  molecules  will  transmit 
this  pressure  to  those  adjacent,  and 
these  to  those  beyond,  until  every 
molecule  of  water  in  the  vessel  exerts 
a  pressure  equal  to  that  exerted  upon 
any  one  of  the  molecules  upon  which 
the  pressure  was  originally  exerted, 
i.  e.,  every  thousand  molecules  in  the 
vessel  will  exert  a  force  of  one  pound. 
Then  will  the  2000  molecules  at  2 
exert  a  force  of  two  pounds  and  the 

3000  molecules  at  3  will  exert  a  force  of  three  pounds. 

219,  An  Important  Principle. — The  foregoing 
argument  may  be  summed  up  as  follows:     When  fluids 
are  subjected  to  pressure,  the  pressure  sustained  bij 
any  part  of  the  restraining  surface  is  proportional 
to  its  area. 

220.  Experimental  Proof.— The  above  principle, 
which  we  deduced  from  Pascal's  law,  may  be  verified  by  ex- 
periment.   Provide  two  com- 
municating tubes  of  unequal 

sectional  area.    When  water  is 

poured  into  these, it  will  stand 

at  the  same  height  in  both 

tubes.   If  by  means  of  a  piston 

the  water  in  the  smaller  tube 

be  subjected  to  pressure,  the 

pressure  will  force  the  water 

back  into  the  larger  tube  and 

rai  se  its  level  t h  ere.   To  prevent 

this  result,  a  piston  must  be 

fitted  to  the  larger  tube  and  held  there  with  a  force  as 

many  times  greater  than  the  force  acting  upon  the  other 


FIG.  67. 


STDROSTA  TICS. 


119 


piston  as  the  area  of  the  larger  piston  is  times  greater  than 
the  area  of  the  smaller  one.  If,  for  example,  the  smallei 
piston  have  an  area  of  1  sq.  cm.  and 
the  larger  piston  an  area  of  16  sq. 
cm.,  a  weight  of  1  Kg.  may  be  made 
to  support  a  weight  of  16  Kg. 

221.  Pascal's  Experiment 
— Pascal  firmly  fixed  a  very  narrow 
tube  about  30  ft.  high  into  the  head 
of  a  stout  cask.  He  then  filled  the 
cask  and  tube  with  water.  The 
weight  of  the  small  amount  of 
water  in  the  tube,  producing  a  pres- 
sure as  many  times  greater  than 
itself  as  the  inner  surface  of  the 
cask  was  times  greater  than  the 
sectional  area  of  the  tube,  actually 
burst  the  cask. 

FIG.  68.  222.   The   Hydro- 

static  Bellows. — The  hydrostatic  bellows 
consists  of  two  boards  fastened  together  by 
a  broad  band  of  stout  leather f  and  a  small 
vertical   tube  communicating  with  the  in- 
terior.   If  the  tube  have  a  sectional  area  of  1 
sq.  cm.,  the  downward  pressure  at  &,  its  base, 
will  be  one  gram  for  every 
centimeter  of  depth  of  water 
in  the  tube.     If  the  upper 
board,  B,  have  a  surfacj  of 
1000  sq.  cm.  exposed  to  the 
water  in  the  bellows,  it  will 
be  pressed  upward  with   a  FIG.  69. 


120 


HYDR  OSTA  TICS. 


force  of  1000  g.  for  every  gram  of  downward  pressure  at  I. 
If  the  tube  be  2  meters  high,  the  downward  pressure  at  E 
will  be  200  g.  and  the  upward  pressure  exerted  on  B  will 
be  200  g.  x  1000  =  200,000  g.  or  200  Kg. 


FIG.  70. 

223.  The  Hydrostatic  Press.— The  hydrostatic 
press,  often  called  the  hydraulic,  or  Bramah's  press,  acts 
upon  the  same  principle.  It  is  represented  in  perspective 
by  Fig.  70  and  in  section  by  Fig.  71.  Instead  of  the 
downward  pressure  produced  by  the  weight  of  the  water 
in  the  tube,  pressure  is  produced  by  the  force-pump.  In- 
stead of  the  two  boards  and  the  leather  band,  a  large, 


HYDROSTATICS. 


121 


strong  reservoir  and  a  piston,  working  water-tight,  are 
used.  The  substance  to  be  pressed  is  placed  between  K, 
the  head  of  the  piston,  and  an  immovable  plate,  MN.  The 
reservoir  and  the  cylinder  of  the  pump  are  connected 
by  the  tube,  d.  By  the  action  of  the  pump,  the  water  in 
the  cylinder,  A,  is  subjected  to  pressure  and  this  pressure 
is  transmitted  undiminished  to  the  water  in  B.  According 
to  the  law  given  in  §  219,  the  power  exerted  upon  the 
lower  surfaces  of  the  two  pistons  is  proportional  to  their 
respective  areas.  But  the  force  exerted  by  the  water  upon 
the  under  surface  of  the  piston  in  the  pump  is  the  same  as 
the  force  exerted  upon  the  water  by  that  piston,  (equality 
of  action  and  reaction).  The  piston,«,is  generally  worked 
by  a  lever  of  the  second  class,  resulting  in  a  still  further 
gain  of  intensity  of  power.  If  the  power  arm  of  the  lever 
be  ten  times  as  long  as  the  weight-arm,  a  power  of  50  Kg. 
at  the  end  of  the  lever  will  exert  a  pressure  of  500  Kg. 
upon  the  water  in  A.  If  the  piston  in  A  have  a  sectional 
area  of  1  sq.  cm.  and  the  piston  in  B  have  an  area  of  500 
6 


122 


HYDROSTA  TICS. 


sq.  cm.,  then  the  pressure  of  500  Kg.  exerted  by  the  small 
piston  will  produce  a  pressure  of  500  Kg.  x  500  =  250,000 
Kg.  upon  the  lower  surface  of  the  large  piston.  He::oe 
the  following  rule : 

Multiply  the  pressure  exerted  by  the  piston  of  the 
pump  by  the  ratio  between  the  sectional  areas  of 
the  two  pistons. 

(a.)  The  accompanying  figure  shows  a  device  due  to  Ritchie  of 
Boston.  It  consists  of  a  base  B  ;  a  sliding  platform  P  guided  by  two 
vertical  pillars  ;  a  bellows-formed  rubber  bag 
connecting  the  base  and  platform  ;  and  a  bag  or 
flask  F,  fitted  with  a  cap  and  cork .  The  flask  is 
connected  with  the  base  by  flexible  tubing.  A 
weight  W  is  placed  upon  the  platform.  Fill 
the  globe  with  water,  and  elevate  it ;  th^  pres- 
sure of  the  column  will  force  the  water  into  the 
bellows,  raising  the  weight ;  lower  the  globe, 
and  the  weight  will  force  the  water  back 
into  it. 

224:.  Liquid  Pressure  Due  to 
Gravity. — The  pressure  exerted  by 
liquids,  on  account  of  their  weight,  may 
be  downward,  upward,  or  lateral.  Pres- 
sure in  any  other  direction  may  be  re- 
solved into  two  of  these.  "We  shall  now 
briefly  consider  these  three  kinds  of 
liquid  pressure. 


FIG.  72. 


225.  Downward  Pressure. — The  pressure  on 
the  bottom  of  a  vessel  containing  a  liquid,  is  in- 
dependent of  the  quantity  of  the  liquid  or  the 
shape  of  the  vessel,  but  depends  upon  the  depth 
and  density  of  the  fluid  and  the  area  of  the 
bottom. 


123 


(a. )  Pascal  contrived  a  neat  experiment  to  verify  this  principle, 
The  apparatus  consists  of  a  wooden  support  carrying  a  ring  into 
which  may  be  screwed  any  one  of  three  vessels,  one  cylindrical,  one 
widening  upward  and  one  narrowing  upward,  straight  or  bent.  On 
he  lower  side  of  the  ring  is  a  plate  a,  supported  by  a  thread  from 


FIG.  73. 

one  end  of  an  ordinary  balance.  The  other  end  of  the  balance 
carries  a  scale-pan.  Weights  in  the  scale-pan  hold  the  plate  a 
against  the  ring  with  a  certain  force.  Water  is  carefully  poured 
into  M  until  the  pressure  forces  off  the  plate  and  allows  a  little 
of  the  water  to  escape.  A  rod  o  marks  the  level  of  the  liquid 
when  this  takes  place.  Repeating  the  experiment  with  the  same 
weights  in  the  scale-pan,  and  either  P  or  Q  in  the  place  of  M, 
the  plate  will  be  detached  when  the  water  has  reached  the  same 
height  although  the  quantity  of  water  is  much  less. 

226.  Rule  for  Downward  Pressure. — When 
the  cylindrical  .vessel,  mentioned  in  the  last  paragraph,  ia 
filled,  it  is  evident  that  the  downward  pressure  is  equal  to 
the  weight  of  the  contained  liquid.  It  is  further  evident 


1*4 


HYDROSTATICS. 


that  the  weight  of  the  counterpoise  in  the  scale-pan,  the 
weight  of  the  liquid  contained  in  P,  and  the  downward 
pressure  exerted  on  the  plate  by  the  liquid  contained  in 
M,  P,  or  Q  are  equal.  We  therefore  deduce  the  following 
rule: 

To  find  the  downward  pressure  on  a  horizontal 
surface,  find  the  weight  of  an  imaginary  column 
of  the  given  liquid,  whose  base  is  the  same  as  the 
given  surface,  and  whose  altitude  is  the  same  as 
the  depth  of  the  given  surface  below  the  surface 
of  the  liquid. 

Note. — A  cubic  foot  of  water  weighs  about  1000  ounces,  62| 
pounds  (more  exactly  62.43  Ibs.). 

22*7.  Upward  Pressure. — Some  persons  have  dif- 
ficulty in  understanding  that  liquids  have  upward  pres- 
sure. This  upward  pressure  may 
be  illustrated  as  follows :  Take  a 
glass  tube  open  at  both  ends,  hav- 
ing at  its  lower  end  a  glass  or  mica 
disc  supported  from  its  centre 
by  a  thread.  If  this  apparatus 
be  placed  in  water,  the  tube 
being  vertical,  the  upward  pres- 
sure of  the  water  will  hold  the 
disc  in  its  place.  If  the  disc  does 
not  accurately  6t  the  end  of  the 
tube,  water  will  be  forced  into  the 
tube,  and  gradually  fill  it  from 
below.  If  the  disc  does  fit  accu- 
rately, as  is  desirable,  pour  water 
carefully  into  the  tube.  In  either  case,  the  disc  will  be 


FIG.  74. 


HYDROSTATICS. 


125 


held  in  place  against  the  force  of  gravity  until  the  level  of 
the  water  within  the  tube  is  very  nearly  the  same  as  that 
in  the  outer  vessel.  The  disc  will  not  fall  until  the  weight 
of  the  water  in  the  tube  plus  the  weight  of  the  disc  equals 
the  upward  pressure. 

Note. — A  lamp-chimney  answers  the  purpose  of  this  experiment. 
On  the  glass  disc  pour  a  little  fine  emery  powder,  and  on  this  rub 
the  end  of  the  lamp-chimney  until  they  fit  accurately.  The  string 
may  be  fastened  to  the  disc  with  wax. 

228.  Rule   for   Upward   Pressure.— To  find 
the  upward   pressure   on   any  horizontal   surface, 
find  the  weight  of  an  imaginary  column  of  the 
given  liquid  whose  base  is  the  same  as  the  given 
surface,  and  whose   altitude   is  the   same   as   the 
depth  of  the  given  surface  below  the  surface  of 
the  liquid. 

229.  The  Hydrostatic  Paradox.— It  may  seem 
strange  at  first  thought  that  vessels  whose  bottoms  are 
subjected  to  equal  pressure,  like  those  represented  in  Fig. 
75,  do  not  exert  equal  pressures  upon  the  stand  supporting 
tli em;  in  other  words,  that  they  do  not  weigh  the  same. 
The  difficulty  will  be  removed  by  remembering  that  the 
pressure  on  the  bottom  of  the  vessel  is  only  one  of 
the   elements   which  combine    to  produce  the  pres* 
sure    upon     the 

stand.  By  refer- C 
ence  to  the  figure, 
which  represents 
three  vessels  of  un- 
equal capacity  but 
having  equal  pres- 
sures upon  the  bot- 


L    H 


126 


HYDR  OSTA  TICS. 


torn,  it  will  be  seen  that  the  weight  may  be  the  resultant 
of  several  forces,  compounded  according  to  the  first  and 
second  cases  specified  in  §  80. 

230.  Lateral    Pressure.— We  have  already  seen 
that  downward  and  upward  pressure  are  proportional  to 
the  depth  of  the  liquid.     Owing  to  the  principle  of  equal 
transmission  of  pressure  in  all  directions,  the  same  holds 

true  for  lateral  pressure,  the 
effects  of  which  are  some- 
times disastrously  shown  by 
the  giving  way  of  flood-gates, 
dams,  and  reservoirs. 

(a.)  These  effects  of  lateral 
pressure  may  be  safely  illus- 
trated by  a  tall  vessel  provided 
with,  a  stop-cock  near  its  base, 
and  arranged  to  float  upon  the 
water.  When  this  vessel  is  filled 
with  water,  the  lateral  pressure 
at  any  two  points  at  the  same 
depth  and  opposite  each  other 
will  be  equal.  Being  equal  and 
opposite  they  will  neutralize  each  other  and  produce  no  motion.  If 
now  the  stop-cock  be  opened,  the  pressure  at  that  point  tending  to 
drive  the  apparatus  in  a  certain  direction,  say  toward  the  left,  is  re- 
moved ;  the  pressure  at  the  opposite  point  tending  to  drive  the 
vessel  toward  the  right,  being  no  longer  opposed  by  its  equal,  will 
now  produce  motion  and  the  vessel  will  float  in  a  direction  opposite 
to  that  of  the  spouting  water.  Instead  of  being  floated  upon  water, 
the  vessel  may  be  supported  by  a  long  thread.  The  same  principle 
is  illustrated  in  Barker's  Mill.  (Fig.  91.) 

231 .  Rule  for  Lateral  Pressure. — To  find  the 
pressure  upon  any  vertical  surface,  find  the  weight 
of  an  imaginary  column  of  the  liquid  whose  base 
is  equal  to  the  given  surface  and  whose  altitude 
is  the  same  as  the  depth  of  the  centre  of  the  given 
surface  below  the  surface  of  the  liquid. 


FIG.  76. 


H  YDR  OSTA  TICS.  127 


EXERCISES. 

1.  What  will  be  the  pressure  on  a  dam  in  30  feet  of  water,  the 
dam  being  30  feet  long  ? 

2.  What  will  be  the  pressure  on  a  dam  in  6  m.  of  water,  the  dam 
being  10  m.  long  ? 

3.  Find  the  pressure  on  one  side  of  a  cistern  5  feet  square  and  12 
feet  high,  filled  with  water. 

4.  Find  the  pressure  on  one  side  of  a  cistern  2  m.  square  and  4  m. 
high,  filled  with  water. 

5.  A  cylindrical  vessel  having  a  base  of  a  sq.  yd. ,  is  filled  with 
water  to  the  depth  of  two  yards.     What  pressure  is  exerted  upon 
the  base? 

6.  A  cylindrical  vessel  having  a  base  of  a  sq.  m.  is  filled  with  water 
to  the  depth  of  two  meters.     What  pressure  is  exerted  upon  the 
base? 

7.  What  will  be  the  upward  pressure  upon  a  horizontal  plate  a 
foot  square  at  a  depth  of  25  ft.  of  water  ? 

8.  What  will  be  the  upward  pressure  upon  a  horizontal  plate  30 
cm.  square  at  the  depth  of  8  m.  of  water  ? 

9.  A  square  board  with  a  surface  of  9  square  feet  is  pressed 
against  the  bottom  of  the  vertical  wall  of  a  cistern  in  which  the 
water  is  8-|  feet  deep.     What  pressure  does  the  water  exert  upon 
the  board  ? 

10.  A  cubical  vessel  with  a  capacity  of  1728  cubic  inches  is  two- 
thirds  full  of  sulphuric  acid,  which  is  1.8  times  as  heavy  as  water. 
Find  the  pressure  on  one  side. 

11.  A  conical  vessel  has  a  base  with  an  area  of  237  sq.  cm.     Its 
altitude  is  38  cm.     It  is  filled  with  water  to  the  height  of  35  cm. 
Find  the  pressure  on  the  bottom.  Arts.  8295  g.  ' 

12.  In  the  above  problem,  substitute  inches  for  centimeters,  and 
then  find  the  pressure  on  the  bottom. 

13.  What  would  be  the  total  liquid  pressure  on  a  prismatic  vessel 
containing  a  cubic  yard  of  water,  the  bottom  of  the  vessel  being  2 
by  3  feet? 

14.  The  lever  of  a  hydrostatic  press  is  6  feet  long,  the  piston-rod 
being  1  foot  from  the  fulcrum.     The  area  of  the  tube  is  one-half 
square  inch  ;  that  of  the  cylinder  is  100  square  inches.     Find  the 
weight  that  may  be  raised  by  a  power  of  75  Ibs. 

15.  What  is  the  pressure  on  the  bottom  of  a  pyramidal  vessel 
filled  with  water,  the  base  being  2  by  3  feet,  and  the  height,  5  feet  ? 

16.  What  is  the  pressure  on  the  bottom  of  a  conical  vessel  4  feet 
high  filled  with  water,  the  base  being  20  inches  in  diameter  ? 


128  EQUILIBRIUM. 

Recapitulation.— In  this  section  we  have  considered 
Ineompressibility;  the  Transmission  of  Pres- 
sure with  Explanation  and  Illustration  ;  Pas- 
cal's Law  with  Argument  and  Conclusion 
therefrom;  one  of  Pascal's  Experiments ;  the 
Hydrostatic  Bellows;  the  Hydrostatic  Press; 
Downward  Pressure  with  experimental  illustra- 
tions; Rule  for  computing  downward  pressure ;  Up- 
ward Pressure  with  experimental  illustrations; 
Rule  for  computing  upward  pressure ;  Lateral 
Pressure  with  experimental  illustrations;  Rule  for 
computing  lateral  pressure. 


ECTfON  H, 


V. 

EQUILIBRIUM.— CAPILLARITY.— BUOYANCY. 

232.  Conditions   of  Liquid  Rest.— The   force 
of  gravity  tends  to  draw  all  liquid  particles  as  near  the 
earth's  centre  as  possible.     The  following  are  necessary 
conditions,  that  a  liquid  may  be  at  rest : 

(1.)  The  free  surface  of  the  liquid  must  be 
everywhere  perpendicular  to  the  force  of  gravity, 
i.  e.,  horizontal.  In  the  case  of  the  ocean,  this  condition 
is  modified  by  the  so-called  centrifugal  force,  which  gives 
rise  to  the  spheroidal  shape  of  the  earth. 

(2.)  Every  molecule  must  ~be  subjected  to  equal 
and  contrary  pressures  in  every  direction. 

233.  Equilibrium    of    Liquids.— A    liquid    of 
small  surface  area  is  said  to  be  level  when  all  the  points  of 


EQUILIBRIUM. 


129 


its  surface  are  in  the  same  horizontal  plane, 
idea  is  expressed  in  the 
familiar  saying,  water 
seeks  its  level.  This 
is  true  whether  the 
liquid  be  placed  in  a 
single  vessel  or  in  sev- 
eral vessels  that  com- 
municate with  each 
other. 


234:.  Communi- 
cating   Vessels. — 

When    any    liquid    is 
placed  in  one  or  more 


The  central 


FIG.  77. 


of  several  vessels  communicating  with  each  other,  it  will 
not  come  to  rest  until  it  stands  at  the  same  height 
in  all  of  the  vessels,  so  that  all  of  the  free  surfaces  lie 
in  the  same  horizontal  plane.  This  principle  is  prettily 
illustrated  by  the  apparatus  represented  in  Fig.  77.  It 
consists  of  such  communicating  vessels  containing  a  liquid. 

(a.)  This  important  principle  that  "  water  seeks  its  level"  finds  a 
gigantic  illustration  in  the  system  of  water-pipes  by  which  water  is 
distributed  in  cities  and  large  towns.  Brought  or  pumped  into  an 
elevated  reservoir  near  the  city,  the  water  flows,  in  obedience  to  the 
force  of  gravity,  through  all  the  turns  and  windings  of  all  the  pipes 
connected  with  the  reservoir,  and  is  thus  brought  into  thousands  of 
buildings.  Into  any  of  the  rooms  of  any  of  these  houses  the  water 
may  thus  be  led,  provided  only  that  the  ends  of  the  pipes  be  below 
the  level  of  the  water  in  the  reservoir. 

(6.)  Among  the  many  other  results  of  this  tendency  of  water  to 
seek  its  level  may  be  mentioned  the  action  of  springs  and  Artesian 
wells,  the  use  of  locks  on  canals,  the  spirit-level,  the  flow  of 
streams,  etc. 


130  CAPILLARITY. 

235.  Capillary  Attraction.  —  The  statements 
made  concerning  the  equilibrium  of  liquids  are  subject  to 
one  important  modification.  When  the  vertical  sides  of 
the  containing  vessel  are  very  near  each  other,  as  in  the 
case  of  small  tubes,  we  have  a  manifestation  of  what  is 
called  capillary  attraction. 

236.  Capillary  Phenomena.— If  a  clean  glass 
rod  be  placed  vertically  in  water,  the  water  will  rise  above 
its  level .  at  the  sides  of  the  glass.  If  the  rod  be  now 
plunged  into  mercury,  this  liquid  will  be  depressed  instead 
of  raised.  If  the  experiments  be  repeated,  it  may  be  noticed 
that  the  water  wets  the  glass  while  the  mercury  does  not. 
If  the  glass  be  smeared  with  grease  and  placed  in  water, 
the  surface  of  the  water  will  be  depressed ;  if  a  clean  lead 
or  zinc  plate  be  placed  in  the  mercury  the  surface  of  the 


FIG.  78. 

mercury  will  be  raised.  In  this  case  the  greased  glass  will 
come  out  dry,  no  water  adhering  to  it,  while  mercury  will 
adhere  to  the  lead  or  zinc.  This  is  found  to  be  invariably 
true:  all  liquids  that  will  wet  the  sides  of  solids 
placed  in  thein  will  be  lifted,  while  those  that  do 
not  will  be  pushed  down.  In  the  figure,  a  represents 


ARCHIMEDES'   PRINCIPLE.  131 

a  glass  rod  in  water ;   b,  a  glass  tube  in  water ;  and  c,  a 
glass  tube  in  mercury. 

(a.)  This  so-called  attraction  is  said  to  be  "  capillary "  because 
its  phenomena  are  best  shown  in  tubes  as  fine  as  a  hair  (Latin, 
capttlus).  If  fine  glass  tubes  be  placed  in  water,  the  liquid  will 
rise,  wet  the  tube,  and  have  a  concave  surface.  If  they  be  placed  in 
mercury,  the  liquid  will  be  depressed,  will  not  wet  the  tube,  and 
will  have  a  convex  surface.  The  finer  the  tube,  the  greater  the 
capillary  ascent  or  depression. 

237.  Displacement  of  a  Fluid  by  an  Im- 
mersed Solid. — A  solid  immersed  in  a  fluid  will 
displace  exactly  its  own  bulk  of  the  fluid.    This  may 
be  proved,  if  desirable,  by  plunging  a  heavy  body  of  known 
polume,  as  a  cubic  centimeter  of  iron,  into  water  contained 
in  a  glass  vessel  graduated  to   cubic  centimeters.     The 
water  will  rise  just  as  if  another  cubic  centimeter  of  water 
had  been  added.     Thus,  the  volume  of   any  irregularly 
shaped  body  may  be  found. 

238.  Archimedes'    Principle.— The    loss    of 
weight  of  a  body  immersed  in  a  fluid  equals  the 
iveijSht  of  the  fluid  which  it  displaces. 

(a.)  It  is  a  familiar  fact  that  a  person  may  easily  raise  to  the  sur- 
face of  the  water  a  stone  which  he  cannot  lift  any  further.  When 
an  arm  or  leg  is  lifted  out  of  the  water  of  a  bath-tub,  there  is  a 
sudden  and  very  perceptible  increase  of  weight  at  the  surface.  Let 
us  try  to  find  a  reason  for  these  familiar  truths.  Imagine  a  cube, 
six  centimeters  on  a  side,  immersed  in  water  so 
that  four  of  its  surfaces  are  vertical  and  its 
upper  horizontal  surface  twelve  centimeters 
below  the  surface  of  the  water.  The  lateral 
pressures  which  the  water  exerts  upon  any  two 
opposite  vertical  surfaces  are  clearly  equal  and 
opposite.  They  will  have  no  tendency  to  move 
the  body.  But  the  vertical  pressures  upon  the 
two  horizontal  surfaces  are  not  equal.  The 
lower  face  will  be  pressed  upward  with  a  force 
represented  by  the  weight  of  (6  x  6  x  18  =)  FIG.  79. 


132  ARCHIMEDES'   PRINCIPLE. 

648  cu.  cm.  of  water  (see  §  228)  while  the  upper  face  will  be  pressed 
downward  with  a  force  represented  by  the  weight  of  (6x6x12  =) 
432  cu.  cm.  of  water.  The  resultant  of  all  these  forces,  therefore, 
will  be  a  net  upward  pressure  represented  by  the  weight  of  (648— 
432=)  216  cu.  cm.  of  water.  But  216  cu.  cm.  is  the  volume  of  the 
cube.  This  net  upward  pressure  or  buoyant  effort  is  exerted  against 
the  force  of  gravity,  and  diminishes  the  weight  of  the  cube. 

239.  An    Experimental    Demonstration. — 

This  principle  of  Archimedes  may  be  experimentally  veri- 
fied as  follows :  From  one  end  of  a  scale-beam  suspend  a 


FIG.  80. 

cylindrical  bucket  of  metal,  b,  and  below  that  a  solid  cyl- 
inder, a,  which  accurately  fits  into  the  bucket.  Counter- 
poise with  weights  in  the  opposite  scale-pan.  Immerse  a 
in  water  and  the  counterpoise  will  descend,  showing  that  a 
has  lost  some  of  its  weight.  Carefully  fill  #  with  water. 
It  will  hold  exactly  the  quantity  displaced  by  a.  Equili- 
brium will  be  restored. 


BUOYANCY.  133 

(a.}  Insert  a  short  spout  in  the  side  of  a  vessel  (as  a  tin  fruit-can) 
about  an  inch  below  the  top.  Fill  the  vessel  with  water  and  let  all 
above  the  level  of  the  spout  escape.  This  is  to  replace  the  vessel 
of  water  in  which  a  (Fig.  80)  is  immersed.  Instead  of  the  bucket, 
&,  use  a  cup  placed  on  the  scale  pan.  Instead  of  a,  use  any  con' 
venient  solid  heavier  than  water,  as  the  fragment  of  a  stone.  Coun- 
terpoise the  cup  and  stone  in  the  air.  Immerse  the  stone  in  the 
water  and  catch,  in  any  convenient  vessel,  every  drop  of  water  that 
overflows.  This  will  be  the  fluid  that  the  solid  displaces.  The 
equilibrium  is  destroyed,  but  may  be  restored  by  pouring  the 
water  just  caught  into  the  cup  on  the  scale-pan. 

24O.  Floating  Bodies.— When  solids  of  different 
densities  are  thrown  into  a  given  liquid,  those  having  den- 
sities greater  than  that  of  the  liquid 
will  sink,  because  the  force  of  gravity 
overcomes  the  buoyancy  of  the  liquid  ; 
those  having  densities  equal  to  that  of 
the  liquid  will  remain  at  rest  in  any 
position  in  the  liquid,  because  the  op- 
posing forces,  gravity  and  buoyancy, 
are  equal;  those  having  densities  less  FIG.  81. 

than  that  of  the  liquid  will  float,  because  the  force  of 
gravity  will  draw  them  down  into  the  liquid  until  they 
displace  enough  of  the  liquid  to  render  the  buoyant  effect 
equal  to  the  weight.  Hence,  a  floating  body  displaces 
its  own  weight  of  the  fluid.  This  may  be  shown  ex- 
perimentally by  filling  a  vase  with  water.  "When  a  float- 
ing body  is  placed  on  the  surface,  the  water  displaced  will 
overflow  and  may  be  caught.  The  water  thus  caught  will 
weigh  the  same  as  the  floating  body. 

(a)  Place  the  tin  vessel  with  a  spout,  mentioned  in  the  last 
article,  upon  one  scale-pan,  and  fill  it  with  water,  some  of  which 
will  overflow  through  the  spout.  When  the  spout  has  ceased 
dripping,  counterpoise  the  vessel  of  water  with  weights  in  the 
other  scale-pan.  Place  a  floating  body  on  the  water.  This  will 


134  BUOYANCY. 

destroy  the  equilibrium,  but  water  will  overflow  through  the  spout 
until  the  equilibrium  is  restored.  This  shows  that  the  floating 
body  has  displaced  its  own  weight  of  water. 

EXERCISES. 

1.  How  much  weight  will  a  cu.  dm.  of  iron  lose  when  placed  in 

water  ? 

2.  How  much  weight  would  it  lose  in  a  liquid  13.6  times  as  heavy 
as  water  ? 

3.  If  the  cu.  dm.  of  iron  weighs  only  7780  g.,  what  does  your 
answer  to  the  3d  problem  signify  ? 

4.  How  much  weight  would  a  cubic  foot  of  stone  lose  in  water  ? 

5.  If  100  cu.  cm.  of  lead  weigh  1135  g.t  what  will  it  weigh  in 
water  ? 

6.  If  a  brass  ball  weigh  83.8  g.  in  air  and  73.8  g.  in  water,  what  is 
its  volume  ? 

7.  If  a  brass  ball  weigh  83.8  oz.  in  air  and  73.8  oz.  in  water,  what 
is  its  volume  ? 

Recapitulation. — In  this  section  we  have  considered 
the  Conditions  of  Liquids  at  Rest ;  the  Equi- 
librium of  liquids  in  Single  and  Communica- 
ting Vessels ;  the  Water  Supply  of  cities ;  the 
Equilibrium  of  Different  Liquids  in  commu- 
nicating vessels ;  Capillary  Attraction  and  some 
of  its  Phenomena  ;  Capillary  Tubes ;  the 
quantity  of  a  Fluid  Displaced  by  an  immersed 
solid;  the  Buoyancy  of  Fluids  ;  Archimedes' 
Principle  ;  several  Explanations  of  Archimedes' 
Principle  and  its  Experimental  Verification  ; 
Floating  Bodies. 


SPECIFIC    GRAVITY.  135 

ECTION  III, 


SPECIFIC    GRAVITY. 

241.  What  is  Specific  Gravity  t—Tke  specific 
gravity  of  a  body  is  the  ratio  betiveen  its  weight 
and  the   weight  of  a  like   volume  of  some  other 
substance  taken  as  a  standard. 

242.  Standard    of    Specific    Gravity.— The 

standard  taken  must  be  invariable.  For  solids  and  liquids, 
the  standard  adopted  is  distilled  water  at  a  tem- 
perature of  4°  C.,  or  39.2°  F.  For  aeriform  bodies,  the 
standard  is  air  or  hydrogen. 

(a.)  The  water  is  to  be  distilled,  or  freed  from  all  foreign  sub 
ftances,  because  the  weight  of  a  given  quantity  of  water  varies  with 
the  substances  held  in  solution.  It  is  to  be  at  a  fixed  temperature 
because  of  the  expansion  by  heat.  The  temperature  above  men- 
tioned is  that  of  water  at  its  greatest  density.  In  cases  where  air  or 
hydrogen  is  taken  as  a  standard,  the  additional  condition  of  atmos- 
pheric pressure  must,  for  obvious  reasons,  be  recognized.  The  pres- 
sure to  which  all  observations  in  this  country  are  reduced  is  that 
recorded  by  30  inches  (760  mm.}  of  the  barometer. 

243.  Elements  of  the  Problem. — For  solids 
or  liquids,  the  dividend  is  the  weight  of  the  given 
body ;    the  divisor  is  the  weight  of  the  same  bulk 
of  water ;  the  quotient,  which  is  an  abstract  number,  is 
the  specific  gravity,  and  signifies  that  the  given  body  is  so 
many  times  heavier  than  the  standard.     The  weight  of  the 
same  bulk  of  water  is  found  sometimes  in  one  way  and 
sometimes  in  another,  but  in  every  case  it  is  the  divisor. 
By  grasping  and  keeping  this  idea,  you  will  avoid  much 
possible  confusion.     Of   course,  when  any  two  of  these 
three  are  given,  the  third  can  be  found* 


136 


SPECIFIC  GRAVITY. 


344.  To  Find  the  Specific  Gravity  of  Solids* 

—  The  most  common  method  of  finding  the  specific  grav- 
ity of  a  solid  heavier  than  water,  is  to  find  the  weight  of 
the  body  in  the  air  (=  W),  then  suspend  the  body  by  a 
light  thread  and  und  its  weight  in  water  (=  W),  and 
divide  the  weight  of  the  body  in  air  by  the  weight  of  the 
same  bulk  of  water  (§  238,  Archimedes'  Principle). 


(a.)  The  method  is  illustrated  by  the  following  example  , 
Weight  of  substance  in  air          =  58£  oz. 
Weight  of  substance  in  water     =  51    oz. 
Weight  of  equal  bulk  of  water  =    7^  oz. 
Specific  gravity  =  58£  oz.  -=-  7£  oz.  =  7.8,  An* 


FIG.  82. 

245.  To  Find  the  Specific  Gravity  of  Solids 
Lighter  than  Water.— If  the  given  body  be  lighter 
than  water,  fasten  to  it  some  body  heavy  enough  to  sink 


SPECIFIC  GRAVITY.  137 

it.  Find  the  loss  in  weight  of  the  combined  mass  when 
weighed  in  water.  Do  the  same  for  the  heavy  body. 
Subtract  the  loss  of  the  heavy  body  from  the  loss  of  the 
combined  body.  Divide  the  weight  of  the  given  body  by 
this  difference.  (Show  that  this  divisor  is  as  indicated  in 
§  243.)  A  modification  of  this  method  is  to  balance  the 
sinker  in  water.  Then  attach  to  it  the  light  substance  in 
question,  e.  g.,  a  cork,  and  determine  the  buoyant  effort  of  the 
cork,  i.  e. ,  the  weight  of  its  bulk  of  water.  Divide  as  before. 

(a.)  The  first  method  is  illustrated  by  the  following  example : 
(1.)  Weight  of  cork  and  iron  in  air 82.4  g. 


(2.) 
(3.) 
(4.) 
(5.) 
(6.) 
(7.) 
(8.) 


"        "       "       water 52.4  g. 

water  displaced  by  cork  and  iron ....  30.    g. 

iron  in  air 77.8  g 

"       water 67.8  g. 

water  displaced  by  iron 10.    g. 

cork  (3)  -  (6). . .  .20.   g 
cork  in  air (1)  —  (4). .    .  4.6  g 


(9.)  Specific  gravity  of  the  cork (8)  -*-  (7) 23 

(10.)          "  "        "       iron (4)  -s-  (6), . . .  7.78 

246.  To    Find    the     Specific    Gravity    of 
Liquids. — The    principle    is    unchanged.      A    simple 
method  is  as  follows:    Weigh  a  flask  first  empty;   next, 
full  of  water  ;  then,  full  of  the  given  liquid.     Subtract  the 
weight  of  the  empty  flask  from  the  other  .two  weights ; 
the  results  represent  the  weights  of  equal  volumes  of  the 
given  substance  and  of  the  standard.    Divide  as  before. 
A  flask  of  known  weight,  graduated  to  measure  100  or 
1000  grams  or  grains  of  water  is  called  a  specific  gravity 
flask.     Its  use  avoids  the  first  and  second  weighings  above 
mentioned,  and  simplifies  the  work  of  division. 

247.  Another  Simple  Method.— The  specific  gravity  of 
a  liquid  may  be  easily  determined  as  follows  :    Find  the  loss  of 
weight  of  any  insoluble  solid  in  water  and  in  the  given  liquid 


138  SPECIFIC  GRAVITY. 

From  §  238,  determine  what  these  two  losses  represent.  Divide  aa 
before.  The  solid  used  is  called  a  specific  gravity  bulb. 

Other  methods  are  sometimes  used,  but  as  they  depend  upon  the 
principles  already  explained,  they  need  not  be  set  forth  here. 
Some  of  them  will  be  illustrated  in  the  problems. 

24:8.  To  Find  the  Specific  Gravity  of  Gases. 

— The  specific  gravity  of  an  aeriform  body  is  always  found 
by  comparing  the  weight  of  equal  volumes  of  the  standard 
(air  or  hydrogen)  and  of  the  given  substance.  The  method 
is  strictly  analogous  to  the  one  first  given  for  liquids.  The 
air  is  removed  from  the  flask  with  an  air-pump — an  in- 
strument to  be  studied  soon.  The  accurate  determination 
of  the  specific  gravity  of  gases  presents  many  practical  dif- 
ficulties which  cannot  be  considered  in  this  place. 

Note. — The  weight  of  any  solid  or  liquid  (in  grams  per  cu.  cm.) 
Tepresents  its  specific  gravity.  Bodies  are  commonly  weighed  in 
the  air.  But,  in  common  with  all  other  fluid  bodies,  the  air  has 
weight  and  therefore  (§  238)  diminishes  the  true  weight  of  all  bodies 
thus  weighed.  This  diminution  is  generally  disregarded,  but  in 
certain  delicate  operations  it  must  be  carefully  considered. 

249.  Hydrometers. — Instruments,  called  hydrom- 
eters or  areometers,  are  made  for  the  more  convenient  de- 
termination of  specific  gravity.    They  dispense  with  the 
use  of  the  balance,  an  instrument  requiring  careful  hand- 
ling and  preservation.    Hydrometers  are  of  two  kinds : 
(1.)  Hydrometers  of  constant  volume,  as  Nicholson's. 
(2.)  Hydrometers  of  constant  weight,  as  Beaume's. 

250.  Nicholson's     Hydrometer.—  Nicholson's 
hydrometer  is  a  hollow  cylinder  carrying  at  its  lower  end 
a  basket  d,  heavy  enough  to  keep  the  apparatus  upright 
when  floated  on  water.     At  the  top  of  the  cylinder  is  a 
vertical  rod  carrying  a  pan  a,  for  holding  weights,  etc. 
The  whole  apparatus  must  be  lighter  than  water,  so  that  a 
certain  weight  (=  W,)  must  be  put  into  the  pan  to  sink 


SPECIFIC   GRAVITY. 


139 


FIG.  83. 

the  apparatus  to  a  fixed  point  marked  on  the  rod  (as  c). 
The  given  body,  which  must  weigh  less  than  W,  is  placed 
m  the  pan,  and  enough  weights  (=  w)  added  to  sink  the 
point  c  to  the  water  line.  It  is  evident  that  the  weight  of 
the  given  body  is  W—  w.  It  is  now  taken  from  the  pan 
and  placed  in  the  basket,  when  additional  weights  (=  x) 
must  be  added  to  sink  the  point  c  to  the  water  line. 

W~w 


Sp.  Gr.  = 
251.  Fahrenheit's 


JC 

Hy- 

drometer. —  Fahrenheit's  Hy- 
drometer is  similar  in  form  to 
Nicholson's,  but  is  made  of  glass 
instead  of  metal,  so  that  it  may 
be  used  in  any  liquid.  The  bas- 
ket is  replaced  by  a  bulb  loaded 
with  shot  or  mercury.  The 
weight  of  the  instrument  (—  W  ) 
is  accurately  determined.  The 
instrument  is  placed  in  water, 


FIG.  84. 


140 


SPECIFIC   GRAVITY. 


and  a  weight  (=  w\  sufficient  to  sink  the  point  c  to  the 
water  line,  is  placed  in  the  pan.  The  weight  of  water  dis- 
placed by  the  instrument  =  W  +  w.  The  hydrometer  is 
now  removed,  wiped  dry,  and  placed  in  the  given  liquid. 
A  weight  (=  z),  sufficient  to  sink  the  hydrometer  to  c,  is 
placed  in  the  pan. 


Nate.  —  A  Nicholson's  hydrometer  may  be  used  as  a  Fahrenheit's 
in  any  liquid  which  has  no  chemical  action  upon  the  metal  of  which 
it  is  made.  Neither  of  these  hydrometers  gives  results  as  accurate 
as  those  obtained  by  the  methods  previously  given. 

252.    Constant    Weight     Hydrometers.—  A 

hydrometer  of  constant  weight  consists  of  a  glass  tube  neai 

the  bottom  of  which  are  two  bulbs.    The  lower  and  smallei 

bulb  is  loaded  with  mercury  or  shot. 

The  tube  and  upper  bulb  containing  air, 

the  instrument  is  lighter  than  water. 

The  point  to  which  it  sinks  when  placed 

in  pure  water  is  generally  marked  zero. 

The  tube  is  graduated  above  and  below 

zero,  the  graduation   bein'g  sometimes 

upon  a  piece  of  paper  placed  within  the 

tube.     As  a  long  stem  would  be  incon- 

venient, it  is  customary  to  have  two  in- 

struments, one  having  zero    near  the 

top,  for  liquids  heavier  than  water  ;  the 

other  having   zero  near  the  bulb,  for 

liquids  lighter  than  water.     The  scale  of  graduation  is  arbi- 

trary, varying  with  the  purpose  for  which  the  instrument  is 

intended.     These  instruments  are  more  frequently  used  to 

determine  the  degree  of  concentration  or  dilution  of  certain 


FIG.  85. 


SPECIFIC   GRAVITY. 


141 


liquids,  as  acids,  alcohols,  milk,  solutions  of  sugar,  etc., 
than  their  specific  gravities  proper.  According  to  their 
uses  they  are  known  as  acidometers,  alcoholometers,  lac- 
tometers, saccharometers,  etc.  They  all  depend  upon  the 
principle  that  a  floating  body  will  displace  its  own  weight 
of  the  liquid  upon  which  it  floats,  and,  consequently,  a 
greater  volume  of  light  than  of  heavy  liquids. 

253.  Tables  of  Reference.— (1.)  Specific  gravities 
of  some  solids : 

Brass...  .  8.38 


Iridium 23.00 

Platinum 22.069 

Gold  (forged)... 19.36 

Lead  (cast) 11.35 

Silver  (cast)....  10. 47 
Copper  (cast). ..  8.79 


Iron  (bar) 7.78 

Tin  (cast) 7.29 

Iron  (cast) 7.21 

Zinc  (cast) 6.86 

Flint  Glass...... 3.33 


Marble  (statuary).  2. 83 
Anthracite  Coal.  .1.80 
Bituminous  Coal.  1.25 

Ice  (melting) 92 

Pine 65 

Cork. .  .  .24 


(2.)  Specific  gravities  of  some  liquids: 


Mercury 13.6 

Sulphuric  Acid..  1.84 
Hydrochloric  Acid  1.24 


Nitric  Acid 1.22 

Milk 1.03 

Sea  Water..    ..1.026 


Turpentine 87 

Alcohol 8 

Ether..  .  .72 


(3.)  Specific  gravities  of  some  gases :    (Barometer  =  760 
mm. -9  Temperature  =  32°  F.  or  0°C.) 


Am  =  STANDARD. 

Hydroiodic  Acid 4.41 

Carbon  Dioxide 1.52 

Oxygen 1.1 

Air 1.0 

Nitrogen 97 

Hydrogen 06* 


HYDROGEN  =  STANDARD. 

Hydroiodic  Acid 64 

Carbon  Dioxide 22 

Oxygen 16 

Air 14.5 

Nitrogen 14 

Hydrogen 1 


Note. — The  weight  of  a  cubic  foot  of  any  solid  or  liquid  is  equal 
to  62.421  Ibs.  avoirdupois  multiplied  by  its  specific  gravity. 

The  weight  of  a  cubic  centimeter  of  any  solid  or  liquid  is  equal 
to  1  gram  multiplied  by  its  specific  gravity. 

The  weight  of  a  liter  (or  cu.  dm.)  of  any  solid  or  liquid  is  equal 
to  1  Kg.  multiplied  by  its  specific  gravity. 

The  tables  above  give  only  average  densities.  Any  given  speci 
men  may  vary  from  the  figures  there  given. 


142 


SPECIFIC  GRAVITY. 


EXERCISES. 

Note. — Be  on  the  alert  to  recognize  Archimedes'  Principle  in 
disguise.  Consider  the  weight  of  water  62|  Ibs.  per  cubic  foot. 

The  numbers  obtained  for  the  right  hand  column  may  be  either 
"olus  or  minus  ;  the  former  sign  denotes  weight  in  the  fluid  ;  the 
/atter,  the  load  it  could  support  in  the  fluid. 


Weight 

Weight 

Loss  of 

Spec. 

ANY 

FLUID. 

in  Air. 

in  Water. 

Weight  in 
Water. 

Grav. 

Volume. 

Sp.  Qr.  of 

Weight  in 

1 

1500  Ibs. 

1000  Ibs. 

? 

? 

?cuft. 

1.5 

? 

2 

5000  oz. 

V 

1500  oz. 

v 

? 

? 

2000  oz. 

3 

? 

1875  g. 

2 

? 

1.8 

9 

4 

? 

9375  g. 

? 

? 

1.5 

4687.5  g. 

5 

? 

? 

7.5 

300  cu.  cm. 

2.5 

! 

6 

? 

1125  Its. 

? 

? 

3 

875  Ibs. 

7 

? 

? 

? 

8  cu.  ft. 

13.6 

2700  Ibe. 

8 

? 

? 

6.86 

5  cu.  dm. 

13.6 

? 

9 

IKg. 

? 

? 

1 

? 

?     . 

200  g. 

20 

? 

? 

? 

2.83 

?0  cu.  ft. 

.8 

? 

11.  A  bone  weighs  2.6  ounces  in  water  and  6.6  ounces  in  air; 
what  is  its  specific  gravity  ? 

12.  A  body  weighing  453  g.  weighs  in  water  429.6  g.;  what  is  its 
specific  gravity  ? 

13.  A  piece  of  metal  weighing  52.35  g.  is  placed  in  a  cup  filled 
with  water.     The  overflowing  water  weighed  5  g.     What  was  the 
specific  gravity  of  the  metal  ? 

14.  (a.)  A  solid  weighing  695  g.  loses  in  water  83  g. ;  what  is  its 
specific  gravity  ;  (6)  how  much  would  it  weigh  in  alcohol  of  specific 
gravity  0.792? 

15.  A  1000  grain  bottle  will  hold  708  grains  of  benzoline.     Find 
the  specific  gravity  of  the  benzoline. 

16.  A  solid  which  weighs  2.4554  oz.  in  air,  weighs  only  2.0778  oz. 
in  water.     Find  its  specific  gravity. 

17.  A  specimen  of  gold  which  weighs  4.6764  g.  in  air  loses  0.2447 
g.  weight  when  weighed  in  water.     Find  its  specific  gravity. 

18.  A  ball  weighing  970  grs.,  weighs  in  water  895  grs.,  in  alcohol 
910  grs.;  find  the  specific  gravity  of  the  alcohol. 

19.  A  body  loses  25  grs.  in  water,  23  grs.  in  oil,  and   19   grs.  in 
alcohol.     Required  the  specific  gravity  of  the  oil  and  the  alcohol. 


SPECIFIC  GRAVITY.  143 

30.  A  body  weighing  1536  g.  weighs  in  water  1283  g.;  what  is  its 
specific  gravity  ? 

21.  Calculate  the  specific  gravity  of  sea  water  from  the  following 

data. 

Weight  of  bottle  empty 8.5305  g. 

"      filled  with  distilled  water....  7.6722  g. 

'   "';,  sea  "      ...  7.7849  g. 

22.  Determine  the  specific  gravity  of  a  piece  of  wood  from  the 
following  data :    Weight  of  wood  in  air,  4  g. ;   weight  of  sinker, 
lOg. ;  weight  of  wood  and  sinker  under  water  8.5  g.;    specific 
gravity  of  sinker,  10.5. 

23.  Apiece  of  a  certain  metal  weighs  3.7395  g.  in  air  ;   1.5780  g. 
in  water  ;  2.2896  g.  in  another  liquid.     Calculate  the  specific  grav- 
ities of  the  metal  and  of  the  unknown  liquid. 

24.  Find  the  specific  gravity  of  a  piece  of  glass  if  a  fragment  of 
it  weigh  2160  grains  in  air,  and  1511^  grains  in  water. 

25.  A  lump  of  ice  weighing  8  Ibs.  is  fastened  to  16  Ibs.  of  lead. 
In  water  the  lead  alone  weighs  14.6  Ibs.  while  the  lead  and  ice  weigh 
13.712  Ibs.     Find  the  specific  gravity  of  the  ice. 

26.  A  piece  of  lead  weighing  600  g.,  weighs  545  g.  in  water  and 
557  g.   in  alcohol.      («.)  Find  the  sp.   gr.  of  the  lead  ;    (&)  of  the 
alcohol,     (c.)  Find  the  bulk  of  the  lead. 

27.  A  person  can  just  lift  a  300  pound  stone  in  the  water  ;  what 
is  his  lifting  capacity  in  the  air  (specific  gravity  of  stone  =  2.5)  ? 

In  the  next  three  examples,  the  weight  of  the  empty  flask  is  not 
taken  into  account. 

28.  A  liter  flask  holds  870  g.  of  turpentine  ;   required  the  sp.  gr. 
of  the  turpentine. 

29.  A  liter  flask,  containing  675  g.  of  water,  on  having  its  remain- 
ing  space  filled  with  fragments  of  a  mineral,  was  found  to  weigh 
1487.5  g. ;  required  the  specific  gravity  of  the  mineral. 

30.  A  liter  flask  was  four-fifths  filled  with  water  ;  the  remaining 
space  being  filled  with  sand  the  weight  was  found  to  be  1350  g.  j 
required  the  specific  gravity  of  the  sand. 

31.  A  weight  of  1000  grs.  will  sink  a  certain  Nicholson's  hydrom- 
eter to  a  mark  on  the  rod  carrying  a  pan.     A  piece  of  brass  plus  40 
grs.  will  sink  it  to  the  same  mark.     When  the  brass  is  taken  from 
the  pan  and  placed  in  the  basket,  it  requires  160  grs.  in  the  pan  to 
sink  the  hydrometer  to  t^e  same  mark  on  the  rod.     Find  the  specific 
gravity  of  the  brass. 

32.  A  Fahrenheit's  hydrometer,  which  weighs  2000  grs.,  requires 
1000  grs.  in  the  pan  to  sink  it  to  a  certain  depth  in  water.    It  requires 
3400  grs.  in  the  pan  to  sink  it  to  the  same  depth  in  sulphuric  acid. 
Find  the  specific  gravity  of  the  acid. 


144  SPECTFIC  ORAVTTT. 

33.  A  certain  body  weighs  just  10  g.    It  is  placed  in  one  of  the 
scale-pans  of  a  balance  together  with  a  flask  full  of  pure  water. 
The  given  body  and  the  filled  flask  are  counterpoised  with  shot  in 
the  other  scale-pan.     The  flask  is  removed,  and  the  given  body 
placed  therein,  thus  displacing  some  of  the  water.     The  flask  being 
still  quite  full  is  carefully  wiped  and  leturned  to  the  scale-pan, 
when  it  is  found  that  there  is  not  equilibrium.      To  restore  the 
equilibrium,  it  is  necessary  to  place  2.5  g.  with  the  flask.     Find  the 
specific  gravity  of  the  given  body. 

34.  The  volume  of   the  earth  is  1,082,842,000,000,000  cu.  Km. 
Calculate  its  weight  on  the  supposition  that  its  average  density  is 
5.6604. 

35.  A  bottle  holds  2545  mg.  of  alcohol  (sp.  gr.  =  0,8095) ;  42740 
mg.  of  mercury  ;  5829  mg.  of  sulphuric  acid.     Calculate  the  specific 
gravities  of  the  mercury  and  of  the  acid. 

86.  A  piece  of  cork  weighing  2.3  g.  was  attached  to  a  piece  of 
iron  weighing  38.9  g.,  both  were  found  to  weigh  in  water  26.2  g.,  the 
iron  alone  weighing  33,9  g.  in  water.  Required  the  specific  gravity 
of  the  cork. 

37.  A  piece  of  wood  weighing  300  grs.  has  tied  to  it  a  piece  of 
Jead  weighing  600  grs.;  weighed  together  in  water  they  weigh  472.5 
grs.     The  specific  gravity  of  lead  being  11.35,  (a)  what  does  the  lead 
weigh  in  water  ;  (&)  what  is  the  specific  gravity  of  the  wood  ? 

38.  Calculate  the  specific  gravity  of  a  mineral   water  from  the 
following  data : 

Weight  of  a  bottle  empty 14.1256  g. 

"  "       filled  with  distilled  water.  .111.1370  g. 

"     mineral      "    .. 111.7050  g. 

89.  A  Fahrenheit's  hydrometer  weighs  618  grs.  It  requires  93  grs. 
in  the  pan  to  sink  it  to  a  certain  mark  on  the  stem.  When  wiped 
dry  and  placed  in  olive  oil  it  requires  only  31  grs.  to  sink  it  to  the 
same  mark.  Find  the  specific  gravity  of  the  oil. 

40.  A  platinum  ball  weighs  330  g.  in  air,  315  g.  in  water  and  303  g. 
in  sulphuric  acid.     Find  the  specific  gravities  (a)  of  the  ball ;  (ft)  of 
the  acid,     (c.)  What  is  the  volume  of  the  ball  ? 

41.  A  hollow  ball  of  iron  weighs  1  Kg.    What  must  be  its  least 
volume  to  float  on  water  ? 

42.  A  piece  of  cork  weighing  30  g.  in  air,  was  attached  to  10  cu. 
cm.  of  lead.    Loss  of  both  in  water  =  159  g.     Required  the  specific 
gravity  of  the  cork. 

43.  A  body  whose  specific  gravity  =  2.8,  weighs  37  g.    Required 
its  weight  in  water. 


Jl  TDK  0  KINETICS*  145 

44.  What  would  a  cubic  foot  of  coal  (sp.gr.  =  2.4)   ^eigh  in  a 
solution  of  potash  (sp.  gr.  =  1.2)? 

45.  A  platinum  ball   (sp.  gr.  =  22)  weighing  300  g.  in  air  will 
weigh  how  much  in  mercury  (sp.  gr.  =  13.6)  ? 

46.  500  cu.  cm.  of  iron,  specific  gravity  7.8,  floats  on  mercury ; 
with  what  force  is  it  buoyed  up  ? 

47.  An  areometer  weighing  600  grs.  sinks  in  water  displacing  a 
volume  =  v ;  in  a  certain  acid,  displacing  a  volume  =  -f$  v ;  find 
the  specific  gravity  of  the  acid. 

Recapitulation. — In  this  section  we  have  considered 
the  Definition  of  Specific  Gravity  ;  the  Stan- 
dards agreed  upon ;  the  Two  Elements  in  specific 
gravity  problems;  the  Rule  for  finding  the  sp.gr.  ol 
Solids  heavier  than  Water  ;  the  same  for  Solids 
lighter  than  Water  ;  the  same  for  Liquids  ;  the 
same  for  Gases ;  the  construction  and  method^  of 
using  Hydrometers  ;  Tables  of  specific  gravities, 
and  some  of  the  uses  that  may  be  made  of  them. 


XgJECTJON    IV, 

H.YDROKI  NETICS. 

254:.   Telocity   of   Spouting    Liquids.— li  a 

vessel  having  apertures  ir.   the   side,  similar  to  the  one 
represented  in  Fig.  86,  be  filled  with  water,  the  liquid  will 
escape  from  each  of  the  apertures,  but  with  different  veloc- 
ities.    Were  it  not  for  the  resistance  of  the  air,  friction, 
and  the  effect  of  the  falling  particles,  the  water  issuing  at 
V  would  ascend  to  the  level  of  the  water  in  the  vessel  j 
i.  e.,  the  initial  velocity  of  the  water  at  V  would  carry  it 
through  the  vertical  distance  Vli.    But  when  equal  verti- 
7 


FIG.  86 

sal  distances  are  passed  over  the  initial  velocity  of  an  ascend 
ing  body  is  the  same  as  the  final  velocity  of  a  falling  body. 
(§  132.)  Hence,  the  velocity  of  the  water  as  it  issues  at  Via 
the  same  that  it  would  acquire  in  freely  falling  the  vertical 
distance  h  V.  This  velocity  is  caused  by  lateral  pressure. 
This  lateral  pressure  will  be  the  same  at  P,  which  is  at  the 
same  distance  below  the  level  of  the  liquid.  Therefore,  the 
velocity  at  P  will  equal  the  velocity  at  V.  Hence  the  fol- 
lowing law:  The  velocity  of  a  stream  flowing  from 
an  orifice  is  the  same  as  that  acquired  by  a  body 
freely  falling  from  a-  height  equal  to  the  head  of 
the  liquid. 

(a.)  The  Tiead  is  the  vertical  distance  from  the  centre  of  the 
orifice  to  the  surface  of  the  liquid. 

(6.)  With  what  velocity  will  water  issue  from  an  orifice  144.72  ft. 
Drtow  the  surface  of  the  liquid  ? 

8  =  \gt*  (§  128  [8].) 

144.72  =  16.08**        /.  9  =  *8. 

8  =  r. 

V  =  fft.  (§  128  [1].) 

t?  =  82.16  ft.  x  3  =  96.48  ft.  An*. 


BTbROKINETICS.  14? 

(<?.)  In  the  solution  above  we  were  obliged  to  find  the  number  of 
seconds  that  would  be  required  for  a  body  to  fall  a  distance  equal 
to  the  head,  before  we  could  use  the  formula  for  the  velocity.  It  is 
desirable,  if  possible,  to  shorten  this  circuitous  process  from  two 
stages  to  one.  This  we  may  do  as  follows  : 


Substituting  this  value  of  t  in  the  formula,  v  =  gtt 


But  li  (the  head)  =  8.  Substituting  this  value  of  8  in  the  last 
equation,  we  have,  for  the  velocity  of  streams  issuing  from  orifices, 
the  following  formula  : 


v  = 

The  value  of  g  being  taken  in  feet,  A  and  -v  must  represent  feet 
also. 

(d.)  With  what  velocity  will  water  issue  from  an  orifice  under  a 
head  of  144.72  feet  ? 
9  =  8.02      fi 


v  =  8.02    /14472~=  8.02  x  12.03  =  96.48,  the  number  of  feet. 

255.  Orifice  of  Greatest  Range.—  The  path  of 
a  stream  spouting  in  any  other  than  a  vertical  direction  is 
the  curve  called  a  parabola  (§  135).  The  range  of  such  a 
stream  will  be  the  greatest  when  it  issues  from  an  orifice 
midway  between  the  surface  of  the  liquid  and  the  level  of 
the  place  where  the  stream  strikes.  Streams  flowing  from 
orifices  equidistant  above  and  below  this  orifice  of  greatest 
range  will  have  equal  ranges  (See  Fig.  86.)  The  range, 
in  any  such  case,  may  be  calculated  by  the  laws  of  pro 
jectiles. 

(a.)  Given  an  aperture  four  feet  below  the  surface  and  20  ft, 
above  the  point  where  the  water  strikes,  to  find  the  range  of  the 
jet 

v  =  8.02  ^/h  =  8.02  x  2  =  16.04  ft.  per  second. 
8=W 

20  =  16.08*8        /.    t  =  1.11  +  sec. 
Range  =  16.04  ft.  x  1.11  =  17.8044  ft. 


148  HYDRO KINETIC '& 

256.  Volume  Discharged  under  a  Constant 
Head. — To  find  the  volume  discharged  in  a  given 
time  under  a  constant  head,  multiply  the  area  of 
the  orifice  by  the  velocity,  and  this  product  ~by  the 
number  of  seconds. 

(a.)  Suppose  that  as  soon  as  the  water  escapes  it  freezes  and  re- 
tains the  form  and  size  given  it  by  the  aperture.  It  will  then  be 
evident  that  the  water  escaping  in  one  second  will  form  a  prism 
whose  section  will  be  the  area  of  the  orifice  and  whose  length  will  be 
the  same  as  the  velocity  of  the  jet.  The  product  of  these  dimensions 
will  give  the  volume  of  the  imaginary  prism,  one  of  which  is  formed 
every  second.  Care  must  be  had  that  the  velocity  and  the  dimen- 
sions of  the  orifice  are  of  the  same  denomination.  The  theoretical 
result  computed  as  above  directed,  will  exceed  the  amount  actually 
discharged.  Why  ?  (See  Appendix  E.) 

251.  The  Flow  of  Liquids  through  Hori- 
zontal Pipes. — When  liquids  from  a  reservoir  are 
made  to  flow  through  pipes  of  considerable  length,  the 
discharge  is  far  less  than  that  due  to  the  head. 
This  is  chiefly  owing  to  the  friction  of  the  liquid  particles 
against  the  sides  of  the  pipe.  A  horizontal  inch-pipe  200 
feet  long  will  not  discharge  much,  if  any,  more  than  a 
quarter  as  much  water  as  a  very  short  pipe  of  the  same 
size,  the  head  heing  the  same.  Frequent  and  abrupt 
bends  in  the  pipe  retard  the  flow,  and  must  be  provided  for 
by  an  increase  in  the  size  of  the  pipe,  or  an  increase  of 
pressure. 

258.  The  Flow  of  Rivers.— The  friction  of  a 
stream  against  its  solid  bed  fortunately  retards  the  velocity 
of  the  water.  Otherwise  the  velocity  of  the  current  at 
the  mouth  of  a  river,  whose  head  is  elevated  1000  feet 
above  its  mouth,  would  be  about  170  miles  per  hour. 
Such  a  current  would  be  disastrous  beyond  description 


HYDR  OKINETICS. 


The  ordinary  river  current  is  from  three  to  five  miles  pel 
hour. 


259.  The  Flow  of 
Liquids  through  Verti- 
cal Pipes.— Liquids  flow  ing 
freely  through  vertical  pipes 
exert  no  lateral  pressure. 
The  liquid  will  not  wholly 
fill  the  tube,  but  will  be  sur- 
rounded by  a  thin  film  of  air. 
These  air  particles  will  be 
dragged  down  by  the  adhe- 
sion of  the  falling  liquid. 

(a.)  If  a  small  tube,  t,  be  inserted 
near  the  top  of  the  vertical  pipe  a 
current  of  air  will  be  forced, 
through  it  and  down  the  pipe. 
This  air  current  may  be  utilized 
for  blow-pipe  and  other  purposes. 
With  a  long  discharge  pipe,  the 
force  with  which  the  air  is  drawn 
through  t  may  be  used  to  remove 
the  air  from  a  vessel.  R.  The  ap- 


FIG.  87. 
paratus  then  becomes  a  Sprengel's  or  Bunsen's  air-pump.  (§§  290, 291.) 


26O.  Water-Power. — Water  may  be  used  to  turn  a 
wheel  and  thus  move  machinery  by  its  weight,  the  force 
of  the  current,  or  both.  The  wheels  thus  turned  are  of 
different  kinds;  the  availability  of  any  one  being  deter- 
mined by  the  nature  of  the  water  supply  and  the  work  to 
be  done. 

(a.}  The  water  supply  depends  upon  rains  ;  rains  depend  upon 
evaporation  ;  evaporation  is  produced  by  solar  heat.  The  energy  of 
water-power  is  thus  traced  to  the  sun  as  its  source, 


150 


HYDR  OKINETICS. 


261.  The    Overshot   Wheel.— In    the  overshot 
wheel,  the  water  falls  into  buckets  at  the  top  and,  by  its 

weight,  aided  by 
the  force  of  the 
current,  turns  the 
wheel.  As  the 

-- 

* ,'  .1  buckets  are  grad- 
ually in  verted,  the 


FIG. 


water  is  emptied 
;  _  }  and  the  load  thus 
removed  from  the 
other  side  of  the 
wheel.  Such 
wheels  require 

only  little  water  but  a  considerable  fall.  It  is  said  that  they 
have  been  made  nearly  100  feet  in  diameter.  The  water 
is  led  to  the  top  of  the  wheel  by  a  sluice,  v  s. 

262.  The  Breast  Wheel.— In  the  breast  wheel, 
the  water  acts  upon  float  boards  fixed  perpendicular  to  the 
circumference.  The  stream  being  received  at  or  near  the 
level  of  the  axis,  both  the  weight 
of  the  water  and  the  force  of 
the  current  may 
be  turned  to 
account. 


FIG.  89. 

263.    The   Undershot   Wheel.— In  the  under- 
shot wheel,  the  stream  strikes,  near  the  bottom  of  the 


H  YDR  OKINETICS. 


151 


wheel,  against  a  few  float  boards,  which  are  more  or  less 

submerged, 
and  thus  acts 
by  the  force  of 
the  current. 

Note. — In  point 
of  efficiency,  these 
wheels  rank  inthe 
order  above  given , 
utilizing  from  80 
FlG-  9°-  to  25  per  cent,  of 

the  total  energy  (e.  g.,  foot-pounds)  of  the  stream. 

264:.    The    Reac- 
tion   Wheel.  —  The 

reaction  wheel  is  well 
illustrated  by  Barker's 
Mill,  represented  in  Fig. 
91.  It  consists  essential- 
ly of  a  vertical  tube  con- 
necting with  horizontal 
tubular  arms  at  the  bot- 
tom. The  ends  of  these 
arms  are  bent  in  the 
same  direction,  and  are 
open  at  their  ends.  The 
apparatus  is  supported 
on  a  pivot  so  as  to  move 
freely.  Water  is  poured 
into  the  upper  end  of  the 
vertical  cylinder,  and  es- 
capes through  the  open- 
ings a  and  b,  at  the  FIG.  91. 
bent  ends  of  the  arms.  The  wheel  revolves  in  a  direction 


152  .  RYDR  OKINETICS. 

opposite  to  that  of  the  water  jets.    The  principle  involved 
was  explained  in  §  230.      (See  Appendix  F.) 

265.  The  Turbine  Wheel.— The  turbine  wheel,  of 
which  there  are  many  varieties,  is  the  most  effective  water- 
wheel  yet  known,  utilizing,  in  some  cases,  85  per  cent,  of 
the  total  energy  of  the  stream. 


FIG.  92. 

(a.)  Fig.  92  represents  one  form  in  perspective  and  in  horizontal 
section  through  the  centre  of  the  wheel  and  case  complete.  The 
wheel  B  and  the  enclosing  case  D  are  placed  on  the  floor  of  a  pen- 
stock wholly  submerged  in  water,  under  the  pressure  of  a  consid- 
erable head.  The  water  enters,  as  shown  by  the  arrows,  through 
openings  in  D,  which  are  so  constructed  that  it  strikes  the  buckets 
of  B  in  the  direction  of  greatest  efficiency.  After  leaving  the 
buckets,  the  "  dead-water "  escapes  from  the  central  part  of  the 
wheel,  sometimes  by  a  vertical  draft  tube,  best  made  of  boiler-iron. 
The  weight  of  the  water  in  this  tube  increases  the  velocity  with 
which  the  water  strikes  the  buckets.  A  central  shaft,  A,  is  carried 
by  the  wheel  and  communicates  its  motion  to  the  machinery  above. 
The  wheel  itself  rests  upon  a  central  pivot  carried  by  cross-arms 
from  the  bottom  of  the  outer  case.  The  case  D  is  covered  with  a 
top  T,  which  protects  the  wheel  from  the  vertical  pressure  of  the 
water.  The  axis  of  the  wheel  passes  through  the  centre  of  this 
cover.  The  openings  by  which  the  water  passes  to  the  wheel  are 
called  chutes.  Sometimes  a  cylindrical  collar,  (7,  is  placed  betweei? 


HYDROKINETICS.  153 

the  wheel  B  and  the  outer  case  D.  This  collar,  called  a  registei 
gate,  may  be  turned  about  its  axis  by  the  action  of  a  pinion,  P, 
upon  teeth  placed  upon  the  circumference  of  (7.  By  means  of  the 
register  gate,  the  size  of  the  chute  may  be  reduced  and  the  amount 
of  water  used  thus  diminished.  The  water  passages,  to  and  from 
the  wheel,  should  be  of  such  a  size  that  the  velocity  of  the  water 
running  through  them  shall  not  exceed  one  and  a  half  feet  per 
^econd. 

266.  Lateral  Pressure  of  Running  Water. 

— If  water  could  flow  through  a  pipe  unimpeded  (v  =  8.02 
A/7*),  there  would  be  no  lateral  pressure.  But  as  the 
velocity  is  lessened  by  friction  and  other  causes,  this  lateral 
pressure  begins  to  be  felt ;  when  the  velocity  is  destroyed, 
lateral  pressure  has  its  full  force  again.  Thus,  a  pipe  is 
less  likely  to  burst  when  carrying  running  water  than  when 
filled  with  water  at  rest. 

267.  Bursting  Pressure.— If  a  current  of  water 
flowing  in  a  pipe  be  suddenly  stopped,  much  of   its  mo- 
mentum will  be  changed  to  lateral  or  bursting  pressure. 
This  takes  place  whenever  the  faucet  of  a  water-pipe  is 
suddenly  closed.    Plumbers  -frequently  leave  the  ends  of 
such  pipes  in  a  vertical  position  so  that  a  quantity  of  air 
may  be  confined  between  the  closed  end  of  the  pipe  and 
the  water  below.     This  air  by  its  elasticity  acts  as  a  pad  or 
cushion,  thus  lessening  the  suddenness  of  the  shock  and 
preventing  accidents.- 

(a.)  This  principle  is  practically  applied  in  the  "  hydraulic  ram," 
a  contrivance  by  which  the  impulse  of  running  water  when  sud- 
denly checked  may  be  used  to  raise  a  part  of  the  water  through  a 
vertical  distance  greater  than  the  head. 

EXERCISES. 

.  1.  A  stream  of  water  issues  from  an  orifice  at  the  bottom  of  a 
vessel  containing  water  169  feet  deep.  Give  the  velocity  of  the 
stream  ? 


154  HTDROKINETICS. 

2.  How  much  water  issues  in  one  hour  from  the  orifice  in  the 
bottom  of  a  vessel  in  which  the  water  always  stands  12  feet  high, 
the  orifice  being  ^  of  a  square  inch  'I 

3.  How  much  water  per  hour  will  be  delivered  from  an  orifice  of 
2   inches  area,  25  feet    below  the    surface  of  a  tank  kept  full,  no 
allowance  being  made  for  friction,  etc.  ? 

4.  From  an  orifice,  water  spouts  with  a  velocity   of  96.24  feet. 
What  is  the  head?  Ans.  144ft. 

5.  An  orifice  is  16.08  feet  above  a  horizontal  floor.     Water  spouts 
to  the  distance  of  80.2  feet.     Required  the  head. 

6.  Determine  the  formula   for   the  velocity  of  spouting  liquids, 
using  meters  instead  of  feet.  Ans.  v  =  4.427  Vh. 

7.  A  stream  of  water  issues  from  an  orifice  under  a  head  of  25 
\neters.     Find  the  velocity  of  the  stream. 

8.  How  many  liters  of  water  will  flow  through  an  opening  of  10 
^q.  cm.  in  20  seconds,  the  head  being  kept  at  86  m.  ?     Ans.  531.24  1. 

9.  How  long  will  it  take  for  442,700  cu.  cm.  of  water  to  escape 
through  a  hole  1  centimeter  square  and  100  meters  below  the  surface 
<>f  the  liquid  Tf 

10.  How  long  will  it  take  to  empty  a  tank  having  a  base  3  m.  by 
4  m.  the  water  being  5  m.  deep,  by  means  of  a  sq.  cm.  hole  in  its 
bottom  ? 

Recapitulation. — In  this  section  we  have  considered 
the  Velocity  of  spouting  liquids ;  the  orifice  of  Great- 
est Range  ;  the  method  of  computing  the  Volume 
discharged  by  an  orifice  when  the  Head  is  con- 
stant ;  the  flow  of  liquids  through  Pipes  and  Rivers  ; 
the  uses  of  Water-power  ;  the  five  kinds  of  Water- 
wheels  ;  the  Lateral  Pressure  of  running  water; 
the  Bursting  Pressure  when  the  current  is  suddenly 
stopped. 

REVIEW  QUESTIONS  AND  EXERCISES. 

1.  (a.)  Define  Physics.      (6.)  Define  and  illustrate  four  universal 
properties  of  matter. 

2.  (a.)  What  is  the  difference  between  momentum  and   energy? 
(&.)  Find  the  momentum  and  (c.)  kinetic  energy   of  a  15  Ib.  ball 
moving  fifty  feet  per  second. 


REVIEW  QUESTIONS.  155 

3.  (a.)  Give  the  third  law  of  motion  and  illustrate  it.    (6.)  Give 
the  law  of  reflected  motion. 

4.  (a.)  What  would  a  1470  Ib.  ball  weigh  at  10,000  miles  above 
the  earth  t    (&.)  Give  the  law  that  you  use. 

5.  (a.)  How  far  will  a  body  fall  during  the  fourth  second?    (b.) 
How  far  in  four  seconds  ?    (c.)  What  will  be  its  final  velocity  ? 

6.  The  crank  of  an  endless  screw  whose  threads  are  an  inch  apart 
describes  a  circuit  of  72  inches.     The  screw  acts  on  the  toothed 
edge  of  a  wheel  whose  circumference  is  90  inches  and  that  of  its  axle 
12  inches.     On  the  axle  is  wound  a  cord  which  acts  on  a  set  of  pul- 
leys three  in  each  block,  the  force  of  which  pulleys  is  exerted  on 
the  wheel  of  a  wheel  and  axle,  the  wheel  being  4  feet  and  the  axle 
8  inches  in  diameter.     What  weight  on  the  axle  will  be  lifted  by  a 
power  of  30  Ibs.  at  the  crank,  allowing  for  a  loss  of  one-third  by 
friction  ? 

7.  (a.)  What  is  the  length  of  a  pendulum  making  25  vibrations  a 
minute  ?    (&.)  How  many  vibrations  are  made  per  minute  by  a  pen- 
dulum 25  inches  long? 

8.  («.)  What  is  a  horse-power  ?    (&.)  A  unit  of  work  ?     (c.)  If  a  two 
horse-power  engine  can  j  ust  throw  1056  Ibs.  of  water  to  the  top  of  a 
steeple  in  2  minutes,  what  is  the  height  of  the  steeple  ? 

9.  (a.)  What  are  the  laws  of  machines?    (&.)  The  facts  concerning 
friction?    (c.)  What  is  a  lever?    (d.)  Figure  a  lever  of  each  kind. 
In  a  lever  of  the  second  kind  the  power  is  4 J,  the  weight  is  40|,  the 
distance  of  the  power  from  the  weight  is  18  in.     (e.)  What  is  the 
length  of  the  lever  ?    (/.)  What  the  length  of  the  short  arm? 

10.  If  the  diameters  of  the  wheel  and  of  the  axle  of  a  wheel  and 
axle  are  respectively  60  in.  and  6  in.,  and  the  power  is  150  Ibs.,  what 
weight  will  be  sustained  ? 

11.  (a.)  Draw  a  system  of  3  fixed  and  2  movable  pulleys.    (&.)  If 
the  power  be  90  and  the  friction  one- third,  what  weight  can  be 
raised? 

12.  (a.)  A  weight  of  12  pounds,  hanging  from  one  end  of  a  five 
foot  lever  considered  as  having  no  weight,  balances  a  weight  of  8 
pounds  at  the  other  end.     Find  how  far  the  fulcrum  ought  to  be 
moved  for  the  weights  to  balance  when  each  is  increased  by  two 
pounds.     (&.)  Give  the  law  for  the  screw  ? 

13.  A  capstan,  14  inches  in  diameter,  has  four  levers  each  7  feet 
long.    At  the  end  of  each  lever  a  man  is  pushing  with  a  force  of 
42  pounds.    What  is  the  effect  produced,  one-fourth  of  the  energy 
expended  being  lost  by  friction  ? 


PNEUMATICS. 


ECTfON 


THE  ATMOSPHERE  AND  ATMOSPHERIC  PRESSURE. 

268.  What  is  Pneumatics  t— Pneumatics  is 
that  branch  of  Physios  which  treats  of  aeriform 
bodies,  their    mechanical  properties,  and  the   ma- 
chines by  which  they  are  used. 

269.  Tension  of  Gases. — However  small  their 
quantity,  gases  always  fill  the  vessels  in  which  they 

are  held.  If  a  bladder  or  India  rub- 
ber bag,  partly  filled  with  air,  and 
having  the  opening  well  closed,  be 
placed  under  the  receiver  of  an  air- 
pump,  the  bladder  or  bag  will  be  fully 
distended,  as  shown  in  the  figure, 
when  the  air  surrounding  the  bladder 
is  pumped  out.  The  flexible  walls 
are  pushed  out  by  the  impact  of  the 
moving  molecules  confined  within.  (See  §  62.) 

270.  The  Type.— As  water  was,  for  obvious  reasons, 
taken  as  the  type  of  liquids,  so  atmospheric  air  will  be 


FIG.  93. 


ATMOSPHERIC  PRESSURE.  157 

taken  as  the  type  of  aeriform  bodies.  Whatever 
mechanical  properties  are  shown  as  belonging  to  air  may 
be  understood  as  belonging  to  all  gases. 

271.  The  Aerial  Ocean. — Air  is  chiefly  a  mixture 
of  two  gases,  oxygen  and  nitrogen,  in  the  proportions  of 
one  to  four  by  volume.     It  is  believed  that  the  atmosphere 
at  its  upper  limit  presents  a  definite  surface  like  that  of 
the  sea ;  that  disturbing  causes  produce  waves  there  just  as 
they  do  on  the  sea,  but  that,  by  reason  of  greater  mobility 
and  other  causes,  the  waves  on  the  surface  of  this  aerial 
ocean  are  much  larger  than  any  ever  seen  on  the  surface 
of  the  liquid  ocean.     The  depth  of  this  aerial  ocean  has 
been  variously  estimated  at  from  fifty  to  two  hundred  miles. 

272.  Weight  of  Air. — Being  a  form  of  matter,  air 
has  weight.    This  may  be  shown  by  experiment.     A  hol- 
low globe  of  glass  or  metal,  having  a  capacity  of  several 
liters  and  provided  with  a  stop-cock,  is  carefully  weighed 
on  a  delicate  balance.    The  air  is  then  removed  from  the 
globe  by  an  air-pump,  the  stop-cock  closed,  and  the  empty 
globe  weighed  carefully.     The  second  weight  will  be  less 
than  the  first,  the  difference  between  the  two  being  the 
weight  of  the  air  removed.     Under  ordinary  conditions  a 
cubic  inch  of  air  weighs  about  0.31  grains  ;    a  liter  of  ail 
weighs  about  1.293  g.,  being  thus  about  -^  as  heavy  ai» 
water.    (See  Appendix  G.) 

273.  Atmospheric    Pressure. — Having  weight, 
such  a  quantity  of  air  must  exert  a  great  pressure  upon 
the  surface  of  the  earth  and  all  bodies  found  there.     This 
atmospheric  pressure  necessarily  decreases  as  we  ascend 
from  the  earth's  surface.     For  any  surface,  at  any  ele- 
vation, the  upward,  downward,  or  lateral  pressure  may  be 


158  ATMOSPHERIC  PRESSURE. 

computed  in  the  same  way  as  for  liquids  (§§  226,  228  and 
231).  Owing  to  the  great  compressibility  of  aeriform 
bodies,  the  lower  layers  of  the  atmosphere  are  much  more 
dense  than  the  upper  ones,  but  density  and  pressure  alike 
are  constant  in  value  throughout  any  horizontal  layer. 
The  weight  of  a  column  of  air  one  inch  square  extending 
i'rom  the  sea-level  to  the  upper  limit  of  the  atmosphere  is 
about  fifteen  pounds;  a  similar  column,  a  cm.  square, 
weighs  about  1  Kg.  We  express  this  by  saying  that  the 
atmospheric  pressure  at  the  sea-level  is  fifteen 
pounds  to  the  square  inch,  or  1  Kg.  to  the  sq.  cm. 
Several  illustrations  of  atmospheric  pressure  will  be  given 
after  we  have  considered  the  air-pump. 

274.  Torricelli's  Experiment.— The  intensity  oi 
this  pressure  may  be  measured  as  fol- 
lows:— Take  a  glass  tube  a  yard  long, 
about  a  quarter  of  an  inch  in  internal 
diameter.  Close  one  end  and  fill  the 
tube  with  mercury.  Cover  the  other 
end  with  the  thumb  or  finger  and  in- 
vert the  tube,  placing  the  open  end 
in  a  bath  of  mercury.  Upon  removing 
the  thumb,  the  mercury  will  sink, 
oscillate,  and  finally  come  to  rest  at 
a  height  of  about  30  inches,  or  760 
mm.)  above  the  level  of  the  mercury 
in  the  bath.  This  historical  experi- 
ment was  first  performed  in  1643, 
by  Torricelli,  a  pupil  of  Galileo. 
The  apparatus  used,  when  properly 
graduated,  becomes  a  barometer,  FIG.  94. 


ATMOSPHERIC  PRESSURE.  159 

275.  What  Supports  the  Mercury  Column  ? 

—To  answer  this  very  important  question,  consider  the 
horizontal  layer  of  mercury  molecules  in  the  tube  at  the 
level  of  the  liquid  in  the  bath.  Under  ordinary  circum- 
stances, they  would  hold  their  position  by  virtue  of  the 
tendency  of  liquids  to  seek  their  level.  But  in  this  case, 
they  hold  it  against  the  downward  pressure  caused  by  the 
weight  of  the  mercury  column  above,  which  is  equivalent 
to  fifteen  pounds  to  the  square  inch.  Being  in  a  condi- 
tion of  equilibrium,  they  must  be  acted  upon  by  an  upward 
pressure  of  fifteen  pounds  to  the  square  inch.  It  is  evident 
that  the  pressure  of  the  mercury  in  the  bath  is  not  able  to 
do  this  work,  its  powers  being  fully  tasked  in  supporting 
the  mercury  in  the  tube  up  to  the  level  of  the  particular 
molecules  now  under  consideration.  This  upward  pres- 
sure then  must  be  due  to  some  force  acting  upon  the  sur- 
face of  tho  mercury,  and  transmitted  undiminished  by  that 
liquid.  The  only  force,  thus  acting,  is  atmospheric 
pressure,  which  is  thus  measured.  The  original  column 
of  thirty-six  inches  fell  because  its  weight  was  greater 
than  the  opposing  force.  As  it  fell,  its  weight  diminished, 
continuing  to  do  so  until  an  equality  of  opposing  forces 
produced  equilibrium.  (See  Appendix  H.) 

276.  Pascal's    Experiments. — Pascal  confirmed 
Torricelli's  conclusions  by  varying  the  conditions.    He 
had  the  experiment  repeated  on  the  top  of  a  mountain  and 
found  that  the  mercury  column  was  three  inches  shorter, 
showing  that  as  the  weight  of  the  atmospheric  column 
diminish es,  the  supported  column  of  mercury  also  dimin- 
ishes.   He  then  took  a  tube  forty  feet  long,  closed  at  one 
end.    Having  filled  it  with  water,  he  inverted  it  over  a 


160 


A  TMO SPHERIC  PRESS  URE. 


water  bath.  The  ivater  in  the  tube  came  to  rest  at 
a  height  of  34  feet.  The  water  column  was  13.6  times 
as  high  as  the  mercury  column,  but  as  the  specific  gravity 
of  mercury  is  13.6,  the  weights  of  the  two  columns  were 
equal.  Experiments  with  still  other  liquids  gave  corres- 
ponding results,  all  of  which  strengthened  the  theory  that 
the  supporting  force  is  due  to  the  weight  of  the  atmos- 
phere, and  left  no  doubt  as  to  its  correctness. 

277.  Pressure  Measured  in  Atmospheres.— 

A  gas  or  liquid  which  exerts  a  force  of  fifteen  pounds  upon 
a  square  inch  of  the  restraining  surface  is  said  to  exert  a 
pressure  of  one  atmosphere.  A  pressure  of  60  pounds  to 
the  square  inch,  or  4  Kg.  to  the  sq.  cm.,  would 
be  called  a  pressure  of  four  atmospheres. 

278.  The  Accuracy  of  a  Barom- 
eter.— The  accompanying  figure  represents 
the  simplest  form  of  the  barometer.     The  in- 
strument's accuracy  depends  upon  the  purity 
of  the  mercury,  the  accuracy  of  measuring  the 
vertical  distance  from  the  level  of  the  liquid 
in  the  cistern  to  that  in  the  tube,  and  the 
freedom  of  the  space  at  the  top  of  the  tube 
from  air  and  moisture.     In  delicate  observa- 
tions allowance  must  be  made  for  differences 
of    temperature.      In     technical    language, 
u  The    barometric    reading    is  corrected   for 
temperature." 

279.  The  Utility  of  a  Barometer. 

—This  instrument's  efficiency  depends  upon 

the  fact  that  variations  in  atmospheric  pres-       FIG.  95. 


ATMOSPHERIC  PRESSURE. 


161 


sure  produce  corresponding  variations  in  the  height  of  the 
barometer  column.  It  is  used  to  determine  the  height  of 
places  above  the  sea-level,  foretell  storms,  etc.  When,  at  a 
given  place,  the  "  barometer  falls,"  a  storm  is  generally 
looked  for.  Sometimes  the  storm  does  not  come,  and 
faith  in  the  accuracy  of  the  instrument  is  shaken.  But,  in 
Fact,  the  barometer  did  not,  announce  a  coming  storm ;  it* 
did  proclaim  a  diminution  of  atmospheric  pres- 
sure from  some  cause  or  other.  Its  declarations  are 
perfectly  reliable ;  inferences  from  those  declarations  are 
subject  to  possible  error. 

280.  The  Aneroid  Barometer. — This  instrument  consists 

of  a  cylindrical  box  of  metal  with  a  top 
of  thin,  elastic,  corrugated  metal.  The 
air  is  removed  from  the  box.  The  top 
is  pressed  inward  by  an  increased 
atmospheric  pressure  ;  whenever  the 
atmospheric  pressure  diminishes,  it  is 
pressed  outward  by  its  own  elasticity 
aided  by  a  spring  beneath.  These 
movements  of  the  cover  are  transmitted 
and  multiplied  by  a  combination  of 
delicate  levers.  These  levers  act  upon 
an  index  which  is  thus  made  to  move 
over  a  graduated  scale.  Such  barome- 
ters are  much  more  easily  portable 
than  the  mercurial  instruments.  They 
are  made  so  delicate  that  they  show 
a  difference  in  atmospheric  pressure 
when  transferred  from  an  ordinary 

to  the  floor.    Their  very  delicacy  involves  the  necessity  for  care- 
ful usage  or  frequent  repairs. 

281.  The    Baroscope. — Air,  having  weight,  has 
buoyant  power.     The  Principle  of  Archimedes  (§  238) 
applies  to  gases  as  well  as  to  liquids.     Prom  this  it  follows 
that  the  weight  of  a  body  in  air  is  not  its  true  weight,  but 
that  it  is  less  than  its  true  weight  by  exactly  the  weight  of 


FIG.  96. 


162 


ATMOSPHERIC  PRESSURE. 


the  air  it  displaces.  This  principle  is  illustrated  by  the 
baroscope,  which  consists  of 
a  scale-beam  supporting  two 
bodies  of  very  unequal  size  (as 
a  hollow  globe  and  a  lead 
ball),  which  balance  one  an- 
other in  the  air.  If  the  appa- 
ratus thus  balanced  in  the  air 
be  placed  under  the  receiver 
of  an  air-pump,  and  the  air 
exhausted,  the  globe  will  de- 
scend, thus  seeming  to  be 
heavier  than  the  lead  ball 
which  previously  balanced  it. 
Is  the  globe  actually  heavier 
than  the  lead,  or  not  ? 


FIG.  97 


EXERCISES. 

1.  Give  the  pressure  of  the  air  upon  a  man  the  surface  of  whose 
body  is  14£  square  feet. 

2.  A  soap-bubble  has  a  diameter  of  4  inches  ;   give  the  pressure 
of  the  air  upon  it.     (See  Appendix  A). 

3.  What  is  the  weight  of  the  air  in  a  room  30  by  20  by  10  feet  ? 

4.  What  will  be  the  total  pressure  of  the  atmosphere  on  a  deci- 
meter cube  of  wood  when  the  barometer  stands  760  mm.  ? 

5.  How  much  weight  does  a  cubic  foot  of  wood  lose  when  weighed 
in  air? 

6.  (a.)  What  is  the  pressure  on  the  upper  surface  of  a  Saratoga 
trunk  2i  by  3^  feet?    (6.)  How  happens  it  that  the  owner  can  open 
the  trunk  ? 

7.  When  the  barometer  stands  at  760  mm.  what  is  the  atmos- 
pheric pressure  per  sq.  cm.  of  surface?  Ans.     1033.6  g. 


Note. — In  round  numbers,  atmospheric  pressure  at  the  sea-level 
U  called  15  Ibs.  to  the  sq.  in.,  or  1  kilogram  to  the  sq.  cm. 


TENSION   OF  GASES.  163 

8.  A  certain  room  is  10  m.  long,  8  m.  wide  and  4  m.  high.    (a.\ 
What  weight  of  air  does  it  contain  ?    (&.)  What  is  the  pressure  upon 
its  floor?     (<?.)  Upon  its  ceiling?     (d.)  Upon  each  end?    (e.)  Upon 
?-ach  side?    (/.)  What  is  the  total  pressure  upon  the  six  surfaces? 
(ff-)  Why  is  not  the  room  torn  to  pieces  ? 

9.  An  empty  toy  balloon  weighs  5  g.     When  filled  with  10  I.  of 
hydrogen,  what  load  can  it  lift  ?   (See  Appendix,  G.) 

Recapitulation. — In  this  section  we  have  considered 
the  definitions  of  Pneumatics  and  Tension  ;  the 
Aerial  Ocean  in  which  we  live ;  the  mechanical 
Properties  of  Air  ;  the  weight  of  air  giving  rise  to 
Atmospheric  Pressure;  a  famous  experiment  by 
TorricelH,and  the  explanation  thereof;  Pascal's  ex- 
periments and  the  conclusion  they  confirmed  ;  the  Ba- 
rometer ;  the  Aneroid  barometer ;  the  Baro- 
scope. 


ECTfON  II. 


THE  RELATION  OF  TENSION  AND  VOLUME  TO 
PRESSURE. 

282.  Tension  of  Gases.— If  a  glass  flask,  provided 
with  a  stop-cock,  be  closed  under  an  atmospheric  pressure 
which  supports  a  mercury  column  of  30  inches,  the  atmos- 
pheric pressure  from  without  is  exactly  balanced  by  the 
tension  (§  269)  of  the  air  within.  If  it  be  closed  under  a 
barometric  pressure  of  28  inches,  this  equality  of  the  two 
pressures  will  continue.  If  the  flask  be  closed  when  the 
surrounding  air  is  subjected  to  a  pressure  of  two  or  three 
atmospheres,  the  equality  will  still  continue.  In  none  of 
these  cases  will  the  glass  be  subjected  to  any  strain  because 


164 


TENSION  OF  OASES. 


of  the  air  within  or  without.  The  tension  of  aeriform 
bodies  supports  the  pressure  exerted  upon  them* 
afid  is  equal  to  it. 

283.  Experimental  Illustrations  of  Tension.— (1.)  The 

tension  of  confined  air  is  well  illustrated  by  the  common  pop-gun 
It  is  also  well  illustrated  by  the  common  experiment 
with  bursting  squares.     These  "squares"  are  made 
of  thin  glass,  are  about  two  or  three  inches  on  each 
edge,  and  are  hermetically  sealed  under  the  ordinary 
atmospheric  pressure.     The  tension  of  the  air  within, 
acting  with  equal  intensity  against  the  atmospheric 
pressure  from  without,  the  frail  walls  remain  unin- 
jured.     When,   however,   the  "square"  is    placed 
under  the  receiver  of  an  air-pump  and  the  external 
pressure  removed,  the  tension  of  15  pounds  to  the 
siuare  inch  is  sufficient  to  burst  the  walls  outward. 
(2.)  Half  fill  a  small  bottle  with  water,  close  the  neck  with  a  cork 
through   which  a  small  tube  passes.     The  lower  end 
of    this  tube  should  dip  into  the  liquid  ;    the  upper 
end  should  be  drawn  out  to  a  smaller  size.     Apply 
the  lips  to  the  upper  end  of  the  tube,  and  force  air 
into  the  bottle.     Notice,  describe,  and    explain  what 
takes  place. 

(3.)  Place  the  bottle,  arranged  as  above  described, 
under  the  receiver  of  an  air-pump,  and  exhaust  the 
air  from  the  receiver.  Water  will  be  driven  in  a  jet 
from  the  tube.  Explain. 


FIG.  98. 


FIG.  99. 


284.  Mariotte's  Law. — The  tempera- 
ture remaining  the  same,  the  volume  of 
a  given  quantity  of  gas  is  inversely  as  the  pres- 
sure it  supports, 

285.— Experimental  Verification  of  Mari- 
otte's Law. — This  law  may  be  experimentally  verified 
with  Mariotte's  tube.  It  consists  of  a  long  glass  tube  bent 
as  shown  in  Fig.  100,  the  long  arm  being  open  and  the 
short  arm  closed.  A  small  quantity  of  mercury  is  poured 
into  the  tube,  so  that  the  two  mercurial  surfaces  are  in  the 


TENSION   OF  GASES. 


165 


FIG.  100. 

horizontal  line.  By  holding  the  tube  nearly  level; 
bubbles  of  air  may  be  passed  into  the  short  arm  or  from  it 
until  the  desired  result  is  secured.  The  air  in  the  short 
arm  will  then  be  under  an  ordinary  atmospheric  pressure. 
As  more  mercury  is  poured  into  the  long  arm  the  confined 
air  will  be  compressed. 

(a.)  When  the  vertical  distance  between  the  levels  of  the  mercury 
in  the  two  arms  is  one-third  the  height  of  the  barometric  column 
at  the  time  and  place  of  the  experiment,  the  pressure  upon  the 
confined  ah  will  be  f  atmospheres  ;  the  tension  of  the  confined  air 


166 


TENSION  OF 


just  supports  this  pressure  and  must  therefore  be  f  atmospheres. 
The  volume  of  the  confined  air  is  only  f  what  it  was  under  a  pres- 
sure of  one  atmosphere.  If  more  mercury  be  poured  into  the  long 
arm  until  the  vertical  distance  between  the  two  mercurial  surfaces 
is  one-half  the  height  of  the  barometric  column,  the  pressure  and 
tension  will  be  f  atmospheres  ;  the  volume  of  the  confined  air  will 
be  |  what  it  was  under  a  pressure  of  one  atmosphere.  When  mer- 
cury has  been  poured  into  the  long  arm  until  the  vertical  distance 
CA  is  equal  to  the  height  of  the  barometric  column,  the  pressure 
and  tension  will  be  two  atmospheres,  and  the  volume  of  the  confined 
air  will  be  one-half  what  it  was  under  a  pressure  of  one  atmos- 
phere. The  law  has  been  thus  "  verified "  up  to  27  atmospheres, 
notwithstanding  which  it  is  not  considered  rigorously  exact.  The 
deviation  from  exactness,  however,  can  be  detected  only  by  meas- 
urement of  great  precision. 

286.  The  Rule  Works  both  Ways.— The  law 
holds  good  for  pressures  of  less  than  one  atmosphere,  for 
rarefied  air  as  well  as  for  compressed 
air.  To  show  that  this  is  true,  nearly 
fill  a  barometer  tube  with  mercury  and 
invert  it  over  a  mercury  bath  held  in  a 
glass  tank  as  shown  in  the  figure. 
Lower  the  tube  into  the  tank  until  the 
mercury  levels  within  the  tube  and 
without  it  are  the  same.  The  air  in  the 
tube  is  confined  under  a  pressure  of  one 
atmosphere.  Note  the  volume  of  air  in 
the  barometer  tube.  Raise  the  tube 
until  this  volume  is  doubled.  The 
vertical  distance  between  the  two  mer- 
curial surfaces  will  be  found  to  be  half 
the  height  of  the  barometric  column. 
The  confined  portion  of  air,  which  is 
now  subjected  to  the  pressure  of  half  an 
FIG.  101.  atmosphere,  occupies  twice  the  space  it 


TENSION  OF  GASES.  16? 

did  under  a  pressure  of  one  atmosphere.  And  so  on.  It 
may  be  more  convenient  to  have  the  barometer  tube  open 
at  both  ends,  the  upper  end  being  closed  with  the  thumb 
or  finger  before  lifting. 

287.  A  Summing  Up. — From  the  foregoing  experi- 
ments we  have  a  right  to  conclude  that  the  density  and 
tension  of  a  given  quantity  of  gas  are  directly,  and 
that  its  volume  is  inversely,  as  the  pressure  ex- 
erted upon  it.  Representing  the  volumes  of  the  same 
quantity  of  gas  by  V  and  v,  and  the  corresponding  pres- 
sures and  densities  by  P  and  p,  D  and  d,  our  conclusion 
may  be  algebraically  expressed  as  follows : 

Z-    P.      ^L 
v  ~~  P  ==  D' 

EXERCISES. 

1.  Under  ordinary  conditions,  a  certain  quantity  of  air  measures 
one  liter.     Under  what  conditions  can  it  be  made  to  occupy  («.)  500 
cu.  cm.  ?    (6.)  2000  cu.  cm.  ? 

2.  Under  what  circumstances  would  10  cu.  inches  of  air  at  the 
ordinary  temperature  weigh  31  grains  ? 

3.  Into  what  space  must  we  compress  (a.)  a  liter  of  air  to  double 
its  tension  ?    (&.)  A  liter  of  hydrogen  ? 

4.  A  barometer  standing  at  30  inches  is  placed  in  a  closed  vessel. 
How  much  of  the  air  in  the  vessel  must  be  removed  that  the  mer- 
cury may  fall  to  15  inches  ? 

5.  A  vertical  tube,  closed  at  the  lower  end,  has  at  its  upper  end 
a  frictionless  piston  which  has  an  area  of  one  sq.  inch.    The  weight 
of  this  piston  is  five  pounds,     (a.)  What  is  the  tension  of  the  air 
in  the  tube?     (&.)  If  the  piston  be  loaded  with  a  weight  of  ten 
pounds,  what  will  be  the  tension  ? 

6.  When  the  barometer  stands  at  28|  inches,  the  mercury  is  at 
the  same  level  in  both  arms  of  a  Mariotte's  tube.     The  barometer 
rises  and  the  difference  in  the  two  mercurial  surfaces  of  the  Ma- 
riotte's tube  is  half  an  inch,    (a.)  In  which  arm  is  it  the  higher  t 
(&.)  Why? 


168  AIR-PUMP. 

7.  Eight  grains  of  air  are  enclosed  in  a  rigid  vessel  of  such  size 
that  the  tension  is  16£  pounds  per  square  inch.  What  will  be  the 
tension  if  three  more  grains  of  air  be  introduced  ? 

Recapitulation.— Iii  this  section  we  have  ^considered 
the  Equality  of  tension  and  pressure,  with  several  Ex- 
perimental Illustrations;  Mariotte's  L,aw; 
the  Verification  of  that  law  for  Compressed 
and  for  Rarefied  Gases;  a  brief  Conclusion  from 
the  teachings  of  these  experiments. 


ECTION  111, 


AIR-PUMPS.— LIFTING   AND    FORCE-PUMPS.— 
SIPHON. 

288.  The  Air-Pump. — The  air-pump  is  an 
instrument  for  removing  air  from  a  closed  vessel. 
The  essential  parts  are  shown  in  section  by  Fig.  102; 
one  form  of  the  complete  instrument  is  represented  by 
Fig.  103. 

The  closed  vessel  R  is  called  a  receiver.  It  fits  accu- 
rately upon  a  horizontal  plate,  through  the  centre  of  which 
is  an  opening  communicating,  by  means  of  a  bent  tube,  /, 
with  a  cylinder,  C.  An  accurately  fitting  piston  moves  in 
this  cylinder.  At  the  junction  of  the  bent  tube  with  the 
cylinder,  and  in  the  piston,  are  two  valves,  v  and  v',  open- 
ing from  the  receiver  but  not  toward  it.  The  tension  of 
the  air  in  R,  and  the  pressure  of  the  air  upon*  the  valves, 
are  equal.  When  the  piston  is  raised,  v'  closes  and  the 
atmospheric  pressure  is  removed  from  v.  The  tension  of 
the  air  in  R  opens  v.  By  virtue  of  its  power  of  indefinite 


AIR-PUMP, 


169 


FIG.  102. 


FIG.  103. 


iWO  AIR-PVMP. 

expansion,  the  air  which,  at  first,  was  in  R  and  t,  now  fills 
R,  t,  and  G.  When  the  piston  is  pushed  down,  v  closes,  v 
opens,  and  the  air  in  0  escapes  from  the  apparatus. 

(a.)  The  lower  valve  ®  is  sometimes  supported,  as  shown  *in  Fig 
102,  by  a  metal  rod  which  passes  through  the  piston.  This  rod 
works  tightly  in  the  piston,  and  is  thus  raised  when  the  piston  is 
raised,  and  lowered  when  the  piston  is  lowered.  A  button  near  the 
upper  end  of  this  rod  confines  its  motion  within  very  narrow  liniitr, 
allows  v  to  be  raised  only  a  little,  and  compels  the  piston,  during 
most  of  the  journeys  to  and  fro,  to  slide  upon  the  rod  instead  of 
carrying  the  rod  with  it. 

289.  Degrees  and  Limits  of  Exhaustion. — 

Suppose  that  the  capacity  of  R  is  four  times  as  great  as 
that  of  C.  (The  capacity  of  t  may  be  disregarded.)  Sup- 
pose that  R  contains  200  parts  of  air  (e.  g.,  200  grains), 
and  (7,  50  parts.  After  lifting  the  piston  the  first  time, 
there  will  be  160  grains  (=  200  x  f)  of  air  in  R,  and  40 
grains  (200  x  \)  in  C.  After  the  second  stroke  there  will 
be  128  grains  [=  160  x  f  =  200  x  f  x  |  =  200  x  (|)2] 
of  air  in  R,  and  32  grains  in  C.  After  n  upward  strokes, 
200  x  (f )"  grains  of  air  will  remain  in  the  receiver.  Evi- 
dently, therefore,  we  never  can,  by  this  means,  re- 
move all  the  air  which  R  contains,  although  we 
might  continually  approach  a  perfect  vacuum,  if  this  were 
the  only  obstacle.  It  requires  an  exceedingly  good  air- 
pump  to  reduce  the  tension  of  the  residual  air  to  -^  inch 
oi.  mercury.  This  limit  is  due  to  several  causes,  among 
which  may  be  mentioned  the  leakage  at  different  parts  of 
the  apparatus,  the  air  given  out  by  the  oil  used  for  lubri- 
cating the  piston,  and  the  fact  that  there  is  a  space  at  the 
bottom  of  the  cylinder  untraversed  by  the  piston. 

290.  Sprengel's  Air-Piimp. — This  instrument  is 
used  to  apply  the  principles  set  forth  in  §  259  to  the  ex- 


AIR-PUMP.  171 

haustion  of  small  receivers.  The  liquid  used  is  mercury. 
The  vertical  pipe,  below  the  arm  t  (Pig.  87),  must  be 
longer  than  the  barometer  column  (six  feet  is  a  common 
length),  and  have  a  diameter  of  not  more  than  -fa  inch. 
The  mercury  is  admitted  by  large  drops,  which,  filling 
the  pipe,  act  as  valves  and  in  their  fall  force  out  succes- 
sive quantities  of  air  before  them. 

(a.)  With  such  an  instrument,  it  requires  about  half  an  hour  to 
exhaust  a  half  liter  receiver,  but  the  average  result  attainable  is  a 
tension  of  about  one-millionth  atmosphere  or  0.00003  inch  of  mer- 
cury. By  this  means  a  tension  of  only  7-3^0^  atmosphere  has 
been  secured.  The  mercury  acts  as  a  dry,  frictionless,  perfectly 
fitting,  self-adj  listing  piston.  Special  precautions  must  be  taken  to 
make  the  connection  air-tight.  The  only  work  of  the  operator  is  to 
carry  the  mercury  from  the  cistern  at  the  foot  of  the  fall  tube  to 
the  funnel  at  the  top. 

291.  Bunseii's    Air-Pump.— In    Bunsen's    air- 
pump  the  principle  is  the  same,  but  the  liquid  used  is 
water,  and  the  length  of  the  vertical  pipe  at  least  thirty- 
four  feet.     Such  an  air-pump  may  be  easily  provided  in  a 
laboratory  where  the  waste-pipe  of  the  sink  has  the  neces- 
sary vertical  height.    The  tube  t  (see  Fig.  87)  being  con- 
nected with  the  receiver,  has  its  free  eiid  inserted  in  the 
waste-pipe  a  little  way  below  the  sink.     A  stream  of  water 
properly  regulated,  flowing  into  the  sink,  completes  the 
apparatus. 

292.  The    Condenser. — The  condenser  is  an 
instrument  for  compressing  a  large  amount  of  air 
into    a   closed   vessel.      It  differs  from  the   air-pump, 
p-hiefly,  in  that  its  valves   open  toward  the  receiver. 
The  cylinder  is  generally  attached  directly  to  the  stop- 
cock of  the  receiver.     Its  operation  will  be  readily  un- 
derstood.     Sometimes    the  upper  valve,  v',   instead  of 


172 


AtR-PUMP. 


being  placed  in  the  piston,  is  placed  in 
a  tube  opening  from  the  side  of  the  cylin- 
der below  the  piston.  By  connecting 
this  lateral  tube  with  a  reservoir  contain- 
ing any  gas,  the  gas  may  be  drawn  from 
the  reservoir  and  forced  into  the  receiver. 
When  thus  made  and  used,  the  instru- 
ment is  called  a  tramferrer  (Fig.  104). 

Note. — The  pupil  will  notice  that  in  the  case 
of  the  air-pump,  the  condenser,  the  transferrer, 
and  the  lifting  and  force  pumps  to  be  subse- 
quently considered,  the  valves  open  in  the  di- 
rection in  which  the  fluid  is  to  move. 


FIG.  104.  293.    Experiments.  —  A    person 

having  an  air-pump  has  the  means  of 
performing  almost  numberless  experiments,  some  amusing 
and  all  instructive.  Other  experiments,  which  may  be  per- 
formed without  such  apparatus,  have  been  purposely  de- 
ferred until  now.  The  pupil  should  explain  each  experiment. 

(1.)  The  pressure  of  the  atmosphere,  which  is  transmitted  in  all 
directions,  may  be  illustrated  by  filling  a  tumbler  with  water,  plac- 
ing a  slip  of  thick  paper  over  its  mouth  and  holding  it  there  while 
the  tumbler  is  inverted  ;  the  water  will  be  supported  when  the 
hand  is  removed  from  the  card. 

(2.)  Plunge  a  small  tube,  or  a  tube  having  a  small  opening  at  the 
lower  end,  into  water,  cover  the  upper  end  with  the  finger  and  lift 
It  from  its  bath.  The  water  is  kept  in  the  tube  by  atmospheric 
pressure.  Remove  the  finger,  and  the  downward  pressure  of  the 
atmosphere,  which  was  previously  cut  off,  will  counterbalance  the 
upward  pressure  and  the  water  will  fall  by  its  own  weight.  Such 
a  tube,  called  a  pipette,  is  much  used  for  transferring  small  quanti- 
ties of  liquids  from  one  vessel  to  another.  The  pipette  is  often 
graduated. 

(3.)  The  "Sucker"  consists  of  a  circular  piece  of  thick  leather 
with  a  string  attached  to  its  middle.  Being  soaked  thoroughly  in 
water  it  is  firmly  pressed  upon  a  flat  stone  to  drive  out  all  air  from 
between  the  leather  and  the  stone.  When  the  string  is  pulled 


AIR-PUMP. 


173 


FIG.  105. 


gently  there  is  a  tendency  toward  the  formation  of  a  vacuum  be- 
tween the  leather  and  the  stone.  The  stone  is 
now  pushed  upward  with  a  force  of  15  Ibs.  foi 
every  square  inch  of  its  lower  surface  (§  273.)  It 
is  pressed  downward  with  a  force  of  15  Ibs.  upon 
each  square  inch  of  its  upper  surface  not  covered  by 
the  "sucker."  The  downward  atmospheric  pres 
sure  upon  the  leather  is  sustained  by  the  string. 
This  difference  between  the  upward  and  down- 
ward atmospheric  pressures  upon  the  stone  may  be 
greater  than  the  gravity  of  the  stone.  Then  we 
say  that  the  stone  is  pulled  up  by  the  "sucker;" 
in  reality  the  stone  is  pushed  up  by  the  air. 

(4.)  The  hand-glass  is  a  receiver  open  at  both 
ends.     The  lower  end  fits  ac- 
curately upon  the  plate  of  the  air-pump.     (It  is 
well  to  smear  the  plate  with  tallow  in  this  and 
similar    experiments.)      The    hand    is    to    be 
placed  over  the  other  end.     When  the  pump  is 
worked,  the  pressure  of  the  atmosphere  is  felt, 
and  the  hand  can  be  removed  only  by  a  con- 
siderable effort.     The  appearance  of  the  palm 
of  the  hand  at  the  end  of  this  experiment  is  due  to  the  tension  ol 
the  air  within  the  tissues  of  the  hand. 
(5.)  Repeat  the  experiment  described  in  §  269. 
(6.)  Over  the  upper  end  of  a  cylindrical  receiver,  tie  tightly  a  wet 
bladder,  and  allow  it  to  dry.     Then  ex- 
haust the  air.     The  bladder  will  be  forced 
inward,  bursting  with  a  loud  noise. 

(7.)  Replace  the  bladder  with  a  piece  of 
thin  india-rubber  cloth.  Exhaust  the  air. 
The  cloth  will  be  pressed  inward  and  nearly 
cover  the  inner  surface  of  the  receiver. 
The  hand-glass,  used  in  experiment  (4), 
will  answer  for  the  two  experiments  last 
given,  by  placing  the  small  end  upon  the 
pump-plate. 

(8.)  Review  the  experiments  mentioned 
in  §  283. 

(9.)  The  "fountain  in  vacua"  consists  of 

a  glass  vessel  through  the  base  of  which  passes  a  tube  terminating 
in  a  jet  within,  and  provided  with  a  stop-cock  and  screw  without. 
By  means  of  the  screw  it  may  be  attached  to  the  air-pump  and  the 


FIG.  107. 


174 


AIR-PUMP. 


FIG.  108. 


FIG.  109. 


air  exhausted.     Remove  the  air,  close  the 

stop-cock,  place  the  lower  end  of  the  tube 

in  water,  open  the  stop -cock  ;  a  beautiful 

fountain  will  be  produced  (Fig.  109). 
(10.)    The    mercury   shower   apparatus 

consists  of  a  cup  through  the  bottom  of 

which  passes  a  plug  of  oak  or  other  porous 
wood.  Place  the  cup  upon 
the  hand-glass  with  a  tum- 
bler below ;  pour  some 
mercury  into  the  cup  ;  ex- 
haust the  air,  and  the  at- 
mospheric pressure  will 
force  the  mercury  through 
the  pores  of  the  wood. 

(11.)     The    weight-lifter 
(Fig.  110)  is  an  apparatus 

by  means  of  which  the  pressure  of  the  atmosphere  may  be  made  to 

lift  quite  a  heavy  weight.     It  consists  of  a  stout  glass  cylinder,  C, 

supported  by  a  frame  and  tripod.     Within  the  lower  part  of  the 

cylinder  is  a  closely  fitting  pis- 
ton from  which  the  weight  is 

hung.     A  brass  plate  is  ground 

to  fit  accurately  upon  the  top 

of  the  cylinder.     This  plate  is 

perforated  and  a  flexible  tube, 

B,  connects  the  cylinder  with 

an   air-pump.     When  the  air 

is  exhausted  from  the   cylin- 
der, the  atmospheric  pressure 

on   the  lower  surface  of   the 

piston   raises   the  piston  and 

supported  weight  the  length 

of  the  cylinder. 

(12.)    The  Magdeburg  hemi- 
spheres  are    made   of   metal. 

They  are  hollow,  and  generally 

three  or  four  inches  in  diam- 

dter.    Their  edges  are  provided 

with  projecting  lips  which  fit 

one  over    the    other.      These 

edges  fit  one  another  air-tight ; 

the   lips  prevent  them    from  FIG.  no. 


LIFTING- PUMP, 


175 


FIG.  in. 


moving  sidewise.  The  edges  being  greased  and  placed  together,  the 
air  is  exhausted  from  the  hollow  globe  through  a  tube  provided 
with  a  stop-cock  and  screw.  When  the  air  has  been 
pumped  out,  close  the  stop-cock,  remove  the  hemi- 
spheres from  the  pump,  and  screw  a  convenient 
handle  upon  the  lower  hemisphere,  the  upper  one 
being  provided  with  a  permanent  handle.  It  will 
be  found  that  a  considerable  force  is  necessary  to 
pull  the  hemispheres  asunder.  This  force  is  equal 
to  the  atmospheric  pressure  upon  the  circular  area 
inclosed  by  the  edges  of  the  hemispheres.  If  this 
area  be  ten  square  inches  it  will  require  a  pull  of 
150  pounds  to  separate  the  hemispheres. 

(13.)  Partly  fill  two  bottles  with  water.  Connect 
them  by  a  bent  tube  which  fits 
closely  into  the  mouth  of  one  and 
loosely  into  the  mouth  of  the  other.  Place  the  bot- 
tles und^r  the  receiver  and  exhaust  the  air.  Water 
will  be  driven  from  the  closely  stoppered  bottle 
into  tb«  other.  Readmit  air  to  the  receiver  and  the 
water  thus  driven  over  will  be  forced  back. 


294.  The  Lifting  FlG  II2 
Pump.— The  lifting- 
pump  consists  of  a  cylinder  or  bar- 
rel, piston,  two  valves,  and  a  suc- 
tion pipe,  the  lower  end  of  which. 
i^  dips  below  the  surface  of  the  liquid 
to  be  raised.  The  arrangement  is 
essentially  the  same  as  in  the  air- 
pump.  As  the  piston  is  worked, 
tho  air  below  it  is  gradually  re- 
moved. The  downward  pressure  on 
the  liquid  in  the  pipe  being  thus 
removed,  the  transmitted  pres- 
sure of  the  atmosphere,  exerted 
upon  the  surface  of  the  liquid, 
pushes  the  liquid  up  through 


FIG.  113. 


176 


FORCE-PUMP. 


the  suction  pipe  and  the  lower  valve  into  the 
barrel.  When  the  piston  is  again  pressed  down,  the  lower 
valve  closes,  the  reaction  of  the  water  opens  the  piston 
valve,  the  piston  sinking  below  the  surface  of  the  liquid  in 
the  barrel.  When  next  the  piston  is  raised,  it  lifts  the 
water  above  it  toward  the  spout  of  the  pump.  At  the  same 
time,  atmospheric  pressure  forces  more  liquid  through  the 
suction  pipe  into  the  barrel. 

295.  Notes  and  Queries. — The  cistern  or  well  containing 
the  liquid  must  not  be  cut  off  from  atmospheric  pressure, i.  e.,  must 
not  be  made  air-tight.  Why  ?  For  water  pumps,  the  suction  pipe 
must  not  be  more  than  34  feet  high.  Why  ?  Owing  to  mechanical 
imperfections  chiefly,  the  practical  limit  of  the  water  pump  is  28 
vertical  feet.  As  the  lifting  of  the  liquid  above  the  piston  does  not 
depend  upon  atmospheric  pressure,  water  may  be  raised  from  a  very 
deep  well  by  placing  the  barrel,  with  its  piston  and  valves,  within 
28  feet  of  the  surface  of  the  water,  and  providing  a  vertical  dis- 
charge pipe  to  the  surface  of  the  ground.  The -piston-rod  may 
work  through  this  discharge  pipe.  Deep  mines  are  frequently 
drained  by  using  a  series  of  pumps,  one 
above  the  other,  the  handles  (levers)  of 
which  are  worked  by  a  single  vertical  rod. 
The  lowest  pump  empties  the  water  into  a 
reservoir,  from  which  the  second  pump  lifts 
it  to  a  second  reservoir,  and  so  on. 

296.  The   Force-Pump.— In 

the  force-pump,  the  piston  is  generally 
made  solid,  i.  e.9  without  any  valve. 
The  upper  valve  is  placed  in  a  dis- 
charge pipe  which  opens  from  the  bar- 
rel at  or  near  its  bottom.  When  the 
piston  is  raised,  water  is  forced  into 
1  the  barrel  by  atmospheric  pressure. 


FIG.  114. 


-— ;-•-  When  the  piston  is  forced  down,  the 
suction  pipe  valve  is  closed,  the  water 


SIPHON. 


177 


being  forced  through  the  other  valve  into  the  discharge 
pipe.  When  next  the  piston  is  raised,  the  discharge  pipe 
valve  is  closed,  preventing  the  return  of  the  water  above 
it,  while  atmospheric  pressure  forces  more  water  from 
below  into  the  barrel. 


FIG.  115. 


297.  The  Air-Chamber  of  a  Force-Pump.— 

Water  will  be  thrown  from  such  a 
pump  in  spurts,  corresponding  to 
the  depressions  of  the  piston.  A 
continuous  flow  is  secured  by 
connecting  the  discharge  pipe 
with  an  air-chamber.  This  air- 
chamber  is  provided  with  a  delivery 
pipe,  #,  the  inner  end  of  which  termi- 
nates below  the  surface  of  the  water 
in  the  air-chamber.  When  water  is 
forced  into  the  air-chamber,  it  covers 
the  mouth  of  the  delivery  pipe  and 
compresses  the  air  confined  in  the 
chamber.  This  diminution  of  volume  of  the  air  is 
attended  by  a  corresponding  increase  of  tension  (§  284), 
which  soon  becomes  sufficient  to  force  the  water  through 
the  nozzle  of  the  delivery  pipe  in  a  continuous  stream. 

298.  The  Siphon. — The  siphon  consists  of  a  bent 
tube,  open  at  both  ends,  having  one  arm  longer  than  the 
other.     It  is  used  to  transfer  liquids  from  a  higher  to  a 
lower  level,  especially  in  cases  where  they  are  to  be  removed 
without  disturbing  any  sediment  they  may  contain.     It 
may  be  first  filled  with  the  liquid,  and  then  placed  with 
the  shorter  arm  in  !t)ie  higher  vessel,  care  being  had  that 
the  liquid  does  not  escape  from  the  tube  until  the  opening 


178  SIPHON. 

O  is  lower  than  mn,  the  surface  of  the  liquid ;  or 
it  may  be  first  placed  in  position, 
and  the  air  removed  by  suction 
at  the  lower  end ;  whereupon,  by 
the  pressure  of  the  atmosphere, 
the  fluid  will  be  forced  up  the 
shorter  arm  and  fill  the  tube.  In 
either  case  a  constant  stream  of 
the  liquid  will  flow  from  the  upper 
PIG  XI6  vessel  until  the  surface  line  mn  is 

brought  as  low  as  the  opening  in 

the  shorter  arm,  or,  if  the  liquid  be  received  in  another 
vessel,  until  the  level  is  the  same  in  the  two  vessels. 

299.  Explanation  of  the  Siphon. — This  action 
of  the  siphon  may  be  thus  explained :    For  convenience, 
suppose  that  the  sectional  area  of  the  tube  is  one  inch, 
that  the  downward  pressure  of  the  water  in  the  arm  AB 
is  one  pound,  and  that  the  downward  pressure  of  the  water 
in  the  arm  BCis  three  pounds.     The  upward  pressure  in 
the  tube  at  A  will  equal  the  atmospheric  pressure  on  each 
inch  of  the  surface  mn  outside  the  tube  minus  the  down- 
ward pressure  of  one  pound,  i.  e.,  (15  —  1  =)  14  pounds, 
On  the  other  side,  there  is  at  0  the  upward  atmospheric 
pressure  of  15  pounds,  from  which   must  be  taken  the 
downward  pressure  of  the  water  in  BC,  leaving  a  resultant 
upward  pressure  of  12  pounds  at  0.    The  upward  pressure 
at  A  being  two  pounds  greater  than  that  at  (7,  determines 
the  flow  of  the  water  A  BC.    The  greater  the  difference 
between  la  and  be,  the  greater  the  velocity  of  the  stream. 

300.  Limitations. — If  the  downward  pressure  at  A 
be  equal  to  the  atmospheric  pressure,  the  liquid  will  not 


SIPHON. 


179 


flow.  Therefore,  if  the  liquid  be  water t  the  height, 
ab,  must  be  less  than  34  feet;  if  it  be  mercury,  db 
must  be  less  than  the  mercury  column  of  the  barometer. 

3O1.  Intermittent  Springs.  —  Occasionally  a 
spring  is  found  which  flows  freely  for  a  time,  and  then 
oeases  to  flow  for  a  time.  Fig.  117  represents  an  under- 
ground reservoir,  fed  with  water  through  fissures  in  the 
earth.  The  channel  through  which  the  water  escapes 


FIG.  117. 


FIG.  118. 


from  this  reservoir  forms  a  siphon.  The  water  escaping  at 
the  surface  constitutes  a  spring.  When  the  water  in  the 
reservoir  reaches  the  level  of  the  highest  point  in  the 
channel,  the  siphon  begins  to  act,  and  continues  to  do  so 
until  the  water  level  in  the  reservoir  falls  to  the  mouth  of 
the  siphon.  The  spring  then  ceases  to  flow  until  the 
water  has  regained  the  level  of  the  highest  point  of  the 
siphon-like  channel.  This  action  is  well  illustrated  by 
"Tantalus'  Cup,"  represented  in  Fig.  118. 

EXERCISES. 

I.  How  high  can  water  be  raised  by  a  perfect  lifting-pump,  Trhen 
the  barometer  stands  at  30  inches  ?    (See  §  253,  [2].) 


180  SIPHON. 

2.  If  a  lifting-pump  can  just  raise  water  28  ft.,  how  high  can  it 
raise  alcohol  having  a  specific  gravity  of  0.8  ? 

3.  Water  is  to  be  taken  over  a  ridge  12.5  m.  higher  than  the  sur- 
face of  the  water,     (a.)  Can  it  be  done  with  a  siphon  ?    Why  ?    (6.) 
With  a  lifting-pump  ?    Why  V    (c.)  With  a  force-pump  ?    Why  ? 

4.  How  high  will  bromine  stand  in  an  exhausted  tube,  when  mer 
cury  stands  755  mm.1    (Sp.  gr.  of  bromine  =  2.06.) 

5.  If  water  rises  34  feet  in  an  exhausted  tube,  how  high  will 
sulphuric  acid  rise  under  the  same  circumstances  ? 

6.  The  sectional  area  of  the  piston  of  a  "  weight-lifter*'  being  1? 
sq.  inches,  what  weight  could  the  instrument  raise  ? 

7.  If  the  capacity  of  the  barrel  of  an  air-pump  is  |  that  of  the  re- 
ceiver, (a.)  what  part  of  the  air  will  remain  in  the  receiver  at  the 
end  of  the  fourth  stroke  of  the  piston,  and  (&.)  how  will  its  tension 
compare  with  that  of  the  external  air  ? 

8.  How  high  could  a  liquid  with  a  sp.  gr.  of  1.35  be  raised  by  a 
lifting-pump  when  the  barometer  stands  29.5  inches  V 

9.  Over  how  high  a  ridge  can  water  be  continuously  carried  in  a 
•iphon,  the  minimum  standing  of  the  barometer  being  69  cm.  ? 

10.  What  is  the  greatest  pull  that  may  be  resisted  by  Magdeburg 
hemispheres  (a.)  4  inches  in  diameter?  (&.)  8  cm.  in  diameter?    (See 
Appendix  A.) 

Recapitulation. — In  this  section  we  have  considered 
the  Air-pump ;  the  Limits  of  Exhaustion  at- 
tainable by  the  ordinary  air-pump ;  Sprengel's  and 
Bunsen's  air-pumps ;  the  Condenser  and  Trans- 
ferrer;  numerous  Experiments  pertaining  to  aeri- 
form pressure  and  tension;  the  Lifting-pump;  the 
Force-pump;  the  Siphon  and  Intermittent 
Springs. 

REVIEW  QUESTIONS  AND  EXERCISES. 

1.  Define  (a.}  Physics,  (&.)  Chemistry,  (c.)  Atom,  (d.)  Molecule,  (<;.) 
Solids,  (/.)  Liquids  and  (0.)  Aeriform  Bodies. 

2.  Define  (a.)  Inertia,  (6.)  Impenetrability  and  (c.)  Hardness,  illua 
trating  each  by  examples. 

3.  (a.)  Define  Momentum  and  (5.)  Energy.     A  body  weighs  500 
Ibs.,  and  has  a  velocity  of  60  ft.  per  second  ;  (c.)  what  is  its  momen 
turn  and  (d.)  what  its  energy  ?     (e.)  How  would  each  be  affected  bj 
doubling  the  weight  ?    (/.)  By  doubling  the  velocity  I 


REVIEW.  181 

4.  Give  (a.)  the  facts  and  (6.)  the  laws  of  gravity.     A  body  weighs 
1440  Ibs.  at  the  surface  of  the  earth  ;  (c.)  how  far  above  the  surface 
will  its  weight  be  90  Ibs.  1     (d.)  What  will  it  weigh  2200  miles 
below  the  surface  ? 

5.  (a.)  What  is  a  machine?    (ft.)  What  is  a  foot  pound?    (c.)  Tell 
how  the  advantage  gained  by  a  simple  mechanical  power  is  found  ; 
md  (d.)  show  this  by  an  illustration  of  your  own.     (e~ )  Explain  the 
jause  of  friction. 

6.  (a.)  What  is  a  simple  pendulum  ?    (6.)  What  is  an  oscillation? 
(c.)  How  does  a  change  of  latitude  change  the  number  of  vibrations  ? 
(d.)  Why? 

7.  (a.)  What  is  the  length  of  a  second's  pendulum  ?    (ft.)  What 
is  the  length  of  one  vibrating  £  seconds  ? 

8.  (a.)  State  the  general  law  of  machines,  and  (ft.)  illustrate  it  by 
means  of  the  pulley. 

9.  (a.)  What  is  the  centre  of  gravity  ?    (ft.)  How  found? 

10.  (a.)  Draw  figures  illustrating  the  position  of  parts  in  the  dif 
ferent  kinds  of  levers ;  (6.)  make  and  solve  a  simple  problem  in 
each. 

11.  (a.)  What  is  the  relation  which  the  length  of  a  pendulum 
bears  to  its  time  of  oscillation  ?    (6.)  Give  the  length  of  a  pendulum 
beating  once  in  2£  seconds. 

12o  (a.)  Give  the  second  and  third  laws  of  motion,  and  (6.)  illus- 
trate them. 

13.  A  and  B,  at  opposite  ends  of  a  bar  6  ft.  long,  carry  a  weight 
of  600  pounds  suspended  between  them.     A's  strength  being  twice 
as  great  as  B's,  how  far  from  A  must  the  weight  be  suspended  ? 

14.  (a.)  Give  the  formulas  for  falling  bodies,  (&.)  translating  them 
into  common  language.      (c.)    Give  the  same    for  bodies  rolling 
freely  down  inclined  planes.     A  body  fell  from  a  balloon  one  mile 
above  the  surface  of  the  earth  ;  (d.)  in  what  time,  and  (e.)  with  what 
velocity  would  it  reach  the  earth  ? 

15.  A  ball  thrown  downward  with  a  velocity  of  35  feet  per  second 
reaches  the  earth  in  12|  seconds,     (a.)  How  far  has  it  moved,  and 
(6.)  what  is  its  final  velocity  ? 

16.  (a.)  A  bricklayer's  laborer  with  his  hod  weighs  170  pounds  ; 
he  puts  into  the  hod  20  bricks  weighing  7  pounds  each ;  he  then 
climbs  a  ladder  to  a  vertical  height  of  30  feet.     How  many  units  of 
work  does  he  ?    (6.)  If  he  can  do  158,100  units  of  work  in  a  day, 
how  many  bricks  will  he  take  up  the  ladder  in  a  day  ? 

17.  Define  three  accessory  properties  of  matter. 

18.  How  much  weight  will  a  cubic  meter  of  any  solid  lose  when 
weighed  (a.)  in  hydrogen?  (6.)  in  air?  (c.)  in  carbonic  acid  gas? 


182  REVIEW. 

19.  Can  you  devise  a  plan  by  which  an  ordinary  mercurial  barom 
eter  may  be  used  to  measure  the  rarefaction  secured  by  an  air-pump  1 

20.  (a.)  Give  the  laws  of  liquid  pressure,  and  (b. )  find  the  pressure 
on  one  side  of  a  cistern  filled  with  water,  5  feet  square  and  12  feet 
high  ? 

21.  (a.)  What  is  specific  gravity?    (&.)  What  the  standard  for 
,'iquids  and  solids?    (e.)  How  is  the  sp.  gr.  of  solids  found? 

22.  Calculate  the  atmospheric  pressure  upon  a  man  having  a  body 
surface  of  16,000  sq.  cm. 

23.  What  is  the  upward  pull  of  a  balloon  of  l,000ew.  m.t  when 
filled  with  gas  half  as  heavy  as  air,  its  own  weight  being  25  Kg. '! 

24.  (a.)  State  Archimedes'  principle.     (&.)  How  may  it  be  experi- 
mentally verified  ?    (c.)  In  finding  specific  gravity,  what  is  always 
the  dividend  and  what  is  always  the  divisor  ?    (d.)  A  specific  gravity 
bulb  weighs  88  g.  in  air,  28  g.  in  water,  and  20  g.  in  an  acid.     Find 
the  sp.  gr.  of  the  acid. 

25.  (a.)  Describe  an  overshot  water-wheel ,  and  (6.)  give  a  drawing. 

26.  (a.)  Define  the  three  kinds  of  equilibrium.     (&.)  Where  is  the 
centre  of  gravity  in  a  ring  ?    (c.)  Why  are  lamps,  clocks,  etc.,  pro- 
vided with  heavy  bases  ? 

27.  Find  the  weight  in  sulphuric  acid  (sp.  gr.  1.75)  of  a  piece  of 
Jead  weighing  150  ^.,  and  having  a  sp.  gi.  of  11. 

28.  A  pendulum   1  meter  long  makes  40  oscillations  in  a  given 
time  ;  how  long  must  a  pendulum  be  to  make  60  oscillations  in  the 
same  time  and  at  the  same  place  ? 

29.  (a.)  Give  Mariotte's  law.     (&.)  How  high  could  a  fluid  having 
a  sp.  gr.  of  1.35  be  raised  in  a  common  pump  when  the  barometer 
stands  at  29.5  inches  ? 

30.  Represent,  by  drawings  in  section,  the  essential  parts  of  (a.) 
an  air-pump,  (&.)  a  lifting-pump,  and  (c.)  a  force-pump,    (d.)  Why 
does  the  water  rise  in  the  suction   pipe  of  a  lifting-pump?    (e.) 
What  is  the  immediate  force  that  throws  water  in  a  steady  stream 
from  a  force-pump  ? 

31.  Water  flows  from  an  orifice  25  feet  below  the  surface  of  the 
water,  and  144.72  feet  above  the  level  ground.     Find  the  range  of 
the  jet. 

32.  State  briefly,  by  diagram  or  otherwise,  the  distinguishing 
features  of  solid,  liquid  and  aeriform  bodies. 

33.  The  specific  gravity  of  1  cu.  ft.  of  wood  is  0.9.     What  is  the 
specific  gravity  of  1  cu,  cm.  ? 


YI. 


V, 

ELECTRICITY     AND     MAGNETISM. 


f. 


GENERAL    VIEW. 

9. — A  desire  to  secure  favorable  atmospheric  conditions  for 
experiments  in  Motional  electricity  has  determined  the  order  in 
which  the  following  branches  of  physics  are  taken  up.  In  most 
places  in  this  country,  the  school-year  begins  with  September.  In 
such  cases,  this  chapter  would  probably  be  reached  by  January, 
during  which  month  the  atmosphere  is  generally  dry.  Under 
other  circumstances,  the  consideration  of  these  subjects  would  better 
be  omitted  until  sound,  heat  and  light  have  been  studied.  The 
experiments  in  this  chapter  are  numbered  consecutively. 

3O2.  Simple  Apparatus. — Provide  two  stout 
sticks  of  sealing-wax  and  one  or  two  pieces  of  flannel  folded 
into  pads  about  20  centimeters  (8  inches)  square;  two 
glass  rods  or  stout  tubes  closed  at  one  end,  30  or  40  centi- 
meters in  length  and  about  2  centimeters  in  diameter  (long 
"ignition  tubes"  will  answer)  and  one  or  two  silk  pads 
about  20  centimeters  square,  the  pads  being  three  or  four 
layers  thick ;  a  few  pith  balls  about  1  centimeter  in  diam- 
eter (whittle  them  nearly  round  and  finish  by  rolling 
them  between  the  palms  of  the  hands)  ;  a  silk  ribbon 
about  an  inch  wide  and  a  foot  long;  a  balanced  straw 


184 


GENERAL    VIEW. 


_ 

FIG.  119. 


about  a  foot  long,  represented  in  Fig.  119.      The  ends 
of  the  straw  carry  two  small  discs  of  paper  (bright  colors 

ry  ^    preferable)  fastened  on  by  sealing-wax. 

^*  ~     "™""^™"    —\j 

The  cap  at  the  middle  of  the  straw  is 
a  short  piece  of  straw  fastened  by  seal- 
ing-wax. This  is  supported  upon  the  point  of  a  sewing- 
needle,  the  other  end  of  which  is  stuck  upright  into  the 
cork  of  a  small  glass  vial.  From  the  ceiling  or  other  con- 
venient support,  suspend  one  of  the  pith  balls  by  a  fine 
silk  thread. 

(a.)  The  efficiency  of  the  silk  pad  above  mentioned  may  be  in- 
creased by  smearing  one  side  with  lard  and  applying  an  amalgam 
made  of  one  weight  of  tin,  two  of  zinc  and  six  of  mercury.  The 
amalgam  that  may  be  scraped  from  bits  of  a  broken  looking-glass 
answers  the  purpose  admirably. 

Experiment  I.  —  Draw  the  silk  ribbon  between  two  layers  of  the 
warm  flannel  pad  with  considerable  friction.  Hold  it  near  the  wall 
of  the  room.  The  ribbon  will  be  drawn  to  the  wall  and  held  there  for 
some  time.  Place  a  sheet  of*  paper  on  a  warm  board  and  briskly 
rub  it  with  india-rubber.  Hold  it  near  the  wall  as  you  did  the  ribbon. 

Experiment  2.  —  Briskly  rub  the  sealing-wax  with  the  flannel 
and  bring  the  wax  near 
the  suspended  pith  ball. 
The  ball  will  be  drawn 
to  the  wax.  Bring  the 
wax  near  one  end  of  the 
balanced  straw  ;  it  may 
be  made  to  follow  the 
wax  round  and  round. 
Bring  it  near  small 
scraps  of  paper,  shreds 
of  cotton  and  silk, 
feathers  and  gold  leaf, 
bran  and  sawdust  and 
other  light  bodies  ;  they  FIG.  120. 

are  attracted  to  tlie  wax. 

Experiment  3.—  Repeat  all  of  these  experiments  with  a  glass  rod 
that  has  been  rubbed  with  the  silk  pad. 


GENERAL    VIEW. 


185 


Experiment  4. — Make  a  light  paper  hoop  or  an  empty  egg-shell 
roll  after  your  rod.     (See  §332  6.) 

Experiment  5. — Place  an  egg  in  a  wine-glass  or  an  egg-cup. 
Upon  the  egg,  balance  a  yard-stick  or  a  common  lath.  The  end  of 
the  stick  may  be  made  to  follow  the 
rubbed  rod  round  and  round.  Place  the 
blackboard  pointer  or  other  stick  in  a 
wire  loop  (Fig.  121)  or  stiff  paper  stir- 
rup suspended  by  a  stout  silk  thread 
or  narrow  silk  ribbon.  It  may  be  made 
to  imitate  the  actions  of  the  balanced 
straw  or  lath.. 


Experiment  6. — Suspend  the  rubbed 
sealing-wax  or  glass  rod  as  you  did 
the  blackboard  pointer  in  the  last  ex- 
periment. Hold  your  hand  near  the 
end  of  the  rod.  It  will  turn  round  and  approach  your  hand. 


FIG.  121. 


Note. — The  pupil  may  be  in- 
genious enough  to  invent  new 
experiments  for  himself  and 
the  class.  The  ability  to  in- 
vent is  often  very  valuable 
and  may  be  acquired  early  in 
life.  Most  of  the  great  in- 
ventors began  making  experi- 
ments when  mere  children. 


3O3.  Electric  At- 
traction. —  TJie  at- 
tractions manifested 
in  the  experiments 
just  described  were 
due  to  electricity  that 
was  developed  l>y  fric- 
tion. Such  electmcity 
is  called  frictional  or  static  electricity. 


FIG.  122. 


186 


GENERAL    VIEW. 


Experiment  7. — Bring  the  rubbed  sealing-wax  or  glass  rod  near 
the  pith  ball  again.  It  will  attract  the  ball  as  before.  Allow  the 
ball  to  touch  the  rod  and  notice  that,  in  a  moment,  the  ball  is 
thrown  off.  If  the  ball  be  pursued  with  the  rod,  it  will  be  found 
that  the  rod  which  attracted  it  a  moment  ago  now  repels  it.  Evidently, 
the  ball  has  acquired  a  new  property.  (Fig.  123. ) 

Experiment  8. — Touch  the  ball  with  the  finger.  It  seeks  the 
rubbed  rod,  touches  the  rod,  flies  from  the  rod.  Repeat  the  experi- 
ments with  the  sealing-wax  after  it  has  been  rubbed  with  flannel. 

Experiment  9. — Rub  the  glass  rod  with  silk  and  bring  it  over 
the  small  scraps  of  paper  as  before.  Notice  that,  after  the  attrac- 
tion, the  paper  bits  do  not  merely  fall  down,  they  are  thrown  down. 


3O4.    Electric 


Repulsion.  —  The  repulsions 
manifested  in  the  experi- 
ments just  described  were 
due  to  static  electricity. 
The  glass  or  wax  is  said  to  be 
electrified  by  friction.  The  ball, 

•  after  obtaining  its  new  property 
of  repulsion  by  coming  in  con- 
tact with  the  glass  or  wax,  is  said 
to  be  electrified  by  conduction. 
The  suspended  pith  ball  is 
called  an  electric  pendulum. 


Experiment  10. — Prepare  a  battery 
solution  according  to  the  recipe  given 
in  §  392,  using  only  half  the  quantity 
of  each  substance  as  therein  directed. 
While  the  solution  is  cooling,  provide  a 
piece  of  sheet  copper  and  one  of  sheet  zinc,  each  about  10  centimeters 
(4  inches)  long  and  4  centimeters  (H  inches)  wide.  To  one  end  of 
each  strip,  solder  (see  Appendix  B)  or  otherwise  fasten  a  piece  of 
No.  18  copper  wire  (See  Appendix  I)  about  15  centimeters  (6  inches) 
long.  Place  the  zinc  strip  in  a  common  tumbler  about  three-fourths 
full  of  the  battery  solution.  Notice  the  minute  bubbles  that  break 
away  from  the  surface  of  the  zinc  and  rise  to  the  surface  of  tlie 


FIG.  123. 


GENERAL    VIEW. 


187 


liquid.  These  are  bubbles  of  hydrogen,  a  combustible  gas.  The 
formation  of  the  gas  is  due  to  chemical  action  between  the  zinc  and 
the  liquid. 

Experiment  II. — Take  the  zinc  from  the  tumbler  and,  while  it  is 
yet  wet,  rub  a  few  drops  of  mercury  (quicksilver)  over  its  surface 
until  it  has  a  brilliant,  silver-like  appearance.  Keplace  the  zinc, 
thus  amalgamated,  in  the  solution  and  notice  that  no  bubbles  are 
given  off. 

Experiment  12.— Place  the  copper  strip  in  the  liquid,  taking  care 
that  it  or  its  wire  does  not  touch  the  zinc  or  its 
wire.  No  bubbles  appear  either  on  the  zinc  or  the 
copper.  It  may  be  convenient  to  place  a  narrow 
glass  strip  between  the  ends  of  the  metal  strips 
in  the  tumbler  to  keep  them  apart. 

Experiment  13. — Bring  the  upper  ends  of  the 
strips  together,  as  shown  in  Fig.  124,  or,  still 
better,  join  the  two  wires,  as  shown  in  Fig.  179, 
being  sure  that  the  wires  are  clean  and  bright 
where  they  are  united.  Notice  the  formation  of 
bubbles  on  the  surface  of  the  copper,  where  none 


3O5.  Suspicion. — It  seems  that  the  connecting 
wire  is  an  important  part  of  the  apparatus  as  now  ar- 
ranged and  we  are  led  to  suspect  that  something  unusual 
is  taking  place  in  the  wire  itself.  It  is  evident  that  we 
have  a  complete  "circuit"  through  the  liquid,  the  metal 
strip  and  the  wire. 

Experiment  14.— Untwist  the  wires  or,  in  other  words,  "  break 
the  circuit."  Connect  the  copper  wires  with  a  short  piece  of  very 
fine  iron  wire.  The  connections  should  be  made  so  that  the  circuit 

shall  include  about  2  centimeters 
(|  inch)  of  iron  wire.  The  iron 
idll  become  hot  enough  to  burn  the 
fingers  or  to  ignite  a  small  quantity 
of  gun  cotton  twisted  around  it. 


FIG.  125. 


Experiment  15. — If  one  of  the 
copper  wires  be  twisted  around  one 
end  of  a  small  file  and.  the  free  end 


188  GENERAL    VIEW. 

of  the  other  wire  be  drawn  along  its  rough  surface,  a  series  of 
minute  sparks  will  be  produced  as  the  circuit  is  rapidly  made  and 
broken. 

Experiment  16.— Place  the  cell  so  that  the  joined  wires  shall  run 
north  and  south,  passing  directly  over  the  needle  of  a  small  com- 
pass (Experiment  98)  and  near  to  it.  The  needle  wttl  instantly  turn  as 
though  it  were  trying  to  place  itself  at  right  angles  to  the  wire. 
Break  the  circuit  and  the  needle  will  swing  back  to  its  north  and 
south  position. 


FIG.  126. 

3O6.  Certainty. — We  now  feel  sure  that  something 
unusual  is  taking  place  in  the  wire  of  our  complete  circuit, 
for  we  have  seen  the  wire  become  hot,  explode  gun-cotton, 
yield  sparks  and  exert  a  very  mysterious  influence  upon 
the  magnetic  needle.  As  a  matter  of  fact,  we  now  have 
a  current  of  electricity  flowing  through  a  voltaic  cell  and 
wire.  Electricity  thus  produced  by  chemical  action 
is  called  voltaic  or  galvanic  electricity.  It  is  one 
form  of  current  electricity. 

Experiment  17. — Wrap  a  piece  of  writing  paper  around  a  large 
iron  nail,  leaving  the  ends  of  the  nail  bare.  Wind  fifteen  or  twenty 
turns  of  stout  copper  wire  around  this  paper  wrapper,  taking  care 
that  the  coils  of  the  wire  spiral  do  not  touch  each  other  or  the  iron. 
It  is  well  to  use  cotton  covered  or  "insulated"  wire.  Connect  the 
two  ends  of  the  wire  spiral  with  the  two  wires  of  the  voltaic  eel] 


GENERAL    VIEW.  189 

or,  in  other  words,  put  the  spiral  into  the  circuit.  Dip  the  end  of 
the  nail  into  iron  filings.  Some  of  the  filings  will  cling  to  the  naU  in 
a  remarkable  manner.  Upon  breaking  the  circuit,  the  nail  instantly 
loses  its  newly  acquired  power  and  drops  the  iron  filings. 

If  the  experiment  does  not  work  satisfactorily,  look  carefully  to 
all  the  connections  of  the  circuit,  see  that  the  ends  of  the  wires  are 
clean  and  bright  and  that  they  are  twisted  together  firmly.  It  may 
be  necessary  to  wash  the  plates,  rub  more  mercury  on  the  zinc  and 
provide  a  fresh  battery  solution. 

307.  Temporary    Magnets. — The  nail  has  the 
power  of  attracting  iron  filings  while  the  electric  cur- 
rent is  flowing  through  the  surrounding  wire  coil. 
You  have  made  an  electro-magnet.     Its  power  of 
attracting  iron  is  called  magnetism.     Satisfy  your- 
self, by  trial,  that  the  nail  loses  its  magnetism  as  soon  as 
the  circuit  is  broken  or  the  current  ceases  to  flow  around 
it.     Remember  that  your  electro-magnet  is  a  temporary 
magnet. 

Experiment  18. — While  the  nail  is  magnetized,  draw  a  sewing- 
needle  four  or  five  times  from  eye  to  point  across  one  end  of  the 
electro-magnet.  Dip  the  needle  into  iron  filings  ;  some  of  them  mil 
cling  to  each  end  of  it. 

308.  Permanent    Magnets.  —  When    steel   is 
treated  as  in  the  last  experiment,  it  becomes  permanently 
magnetized. 

Experiment  19. — Cut  a  thin  slice  from  the  end  of  a  vial  cork  and, 
with  its  aid,  float  your  magnetized  needle  upon  the  surface  of  a 
bowl  or  saucer  of  water.  The  needle  comes  to  rest  in  a  north  and 
south  position.  Turn  it  from  its  chosen  position  and  notice  that,  after 
each  displacement,  it  resumes  the  same  position  and  that  the  same 
end  of  the  needle  always  points  to  the  north. 

309.  A  Simple   Compass.—^  small  magnet- 
ized steel  bar  freely  suspended,  is  called  a  com- 


190  GENERAL    VIEW. 

pass.  The  one  that  you  have  made  may  be  less  conven- 
ient than  is  the  compass  of  the  mariner  or  the  surveyor, 
but  it  is  as  reliable. 

310.  Artificial    Magnets. — The    electro-magnet 
and  the  permanent  magnet  that  you  make  are,  of  course, 
artificial    magnets.      There    is    a    natural    magnet 
known  as  lodestone. 

311.  Other  Forms  of  Current  Electricity. — 

Electric  currents  may  be  generated  by  the  action  of  other 
currents  of  electricity  or  by  the  action  of  magnets.  Elec- 
tricity thus  developed  is  called  induced  electricity.  A 
current  of  thermo-electricity  may  be  generated  by  heating 
the  junction  of  two  metals  that  form  part  or  all  of  a  cir- 
cuit. 

312.  The   Different   Forms    of  Electricity 
are  Identical. — So  far  as  experiment  can  show,  one 
form  of  electricity   may    have  a  particular  property  in 
greater  degree  than  some  other  form,  but  all  are  identical, 
each  having  all  the  properties  of  any  of  the  others. 


GENERAL    VIEW. 


191 


Recapitulation. — To  be  amplified  by  the  pupil  foi 
review. 


H 

r1 

8 
s 

n 


m 


c 


q    w 

H 


II. 


FRICTIONAL  ELECTRICITY  OR  ELECTRIC  CHARGES. 

313.  The  Nature  of  Electricity.  —But  little  is 
known  concerning  the  real  nature  of  electricity.      It  is 
easier  to  tell  what  electricity  can  do  than  to  tell  what  it 
is.     The  majority  of  modern  physicists  consider  that  elec- 
tricity  is  a    form  of   energy    producing    peculiar 
phenomena  ;  that  it  may  be   converted  into  other 
forms    of   energy    and   that    all    other   forms    of 
energy  may  be  converted  into  it.    It  is  believed  that 
electricity  is  a  form  of  molecular  motion,  but  this  belief 
still  rests  upon  analogy  rather  than  demonstration.     Sev- 
eral theories  have  been  advanced  to  account  for  electrical 
phenomena,  but  none  of  them  is  satisfactory. 

314.  Electric     Manifestations.  —  Electricity 
may  reveal  itself  as  a  charge  residing  on  the  sur- 
face of  a  body  or  as  a  current  flowing  through  its 
substance.     By  means  of  friction,  the  glass  rod  or  the 
sealing-wax  (§§  303,  304)  acquired  an  electrical  charge 
and,  consequently,  the  power  of  attracting  and  repelling 
light  bodies  ;  by  means  of  chemical  action,  the  voltaic  dell 
(§  306)  generated  electricity  that  manifested  itself  as  a 
current.     In  this  section,  we  shall  consider  electricity  that 
appears  as  a  charge,  i.e.,  static  electricity. 


FRICTION 'AL   ELECTRICITY. 


193 


(a.)  The  electrified  body  is  said  to  be  charged.  When  the  electric- 
ity is  removed,  the  body  is  said  to  be  discharged.  Good  conductors 
(§  324)  are  instantly  discharged  when  touched  by  the  hand,  or  by  any 
good  conductor  connected  with  the  earth.  A  poor  conductor  may 
be  readily  discharged  by  passing  it  rapidly  through  a  flame,  as  of  a 
lamp  or  candle. 

Experiment  20. — Prepare  two  electric  pendulums.  Bring  the 
electrified  glass  rod  near  the  pith  ball  of  one  ;  after  contact,  the  ball 
will  be  repelled  by  the  glass.  Bring  the  electrified  sealing-wax 
near  the  second  pith  ball  ;  after  contact,  it  will  be  repelled  by  the 
wax.  Satisfy  yourself  that  the  electrified  glass  will  repel  the  first ; 
that  the  electrified  sealing-wax  will  repel  the  second.  Let  the  glass 
rod  and  the  sealing-wax  change  hands.  The  first  ball  was  repelled 
by  the  glass  ;  it  will  be  attracted  by  the  sealing-wax.  The  second  ball 
was  repelled  by  the  sealing-wax ;  it  will  be  attracted  by  the  glass. 

Experiment  21. — Suspend  two  pith  balls  as  shown  in  Fig.  127, 
and  touch  them  with  a  rubbed 
rod.      Instead  of 


con- 
tinuing to  hang  side  by  side, 
they  repel  each  other  and  fly 
apart.  If  the  electrified  glass 
rod  be  held  near  them,  they 
separate  still  further.  If 
the  electrified  sealing-wax, 
instead  of  the  glass,  be  held 
near  them,  they  •will  fall 
nearer  together.  If  the 
rubbed  glass  rod  be  sus- 
pended as  shown  in  Fig.  121, 
it  will  be  repelled  by  another 
rubbed  glass  rod,  but  at- 
tracted by  rubbed  sealing- 
wax. 


FIG.  127. 


315.  Two    Kinds    of  Electricity.  —  The 

tricity  developed  on  glass  is  different  in  kind  from 
that  developed  on  sealing-wax.  They  exhibited  op- 
posite forces  to  a  third  electrified  body,  each  attracting 
what  the  other  repels. 


194  FRICTION AL  ELECTRICITY. 

Experiment  22. — Hold  the  silk  pad  in  a  piece  of  sheet-rubbet 
and,  with  it,  rub  the  glass  rod.  Suspend  the  glass  rod  and  bring 
the  silk  pad  near  it.  The  electrified 
pad  will  attract  the  glass,  but  will 
repel  a  suspended  stick  of  sealing-wax 
that  has  been  rubbed  with  flannel. 

316.  Electric  Separa- 
tion.— All  electrified  bodies 
net  like  either  tine  glass  or  the 
sealing-wax.  When  the  glass 
rod  was  positively  electrified,  an 
F  8  equal  amount  of  negative  elec- 

tricity was  simultaneously  devel- 
oped in  the  silk  with  which  it  was  rubbed.  When  the  seal- 
ing-wax was  negatively  electrified,  an  equal  amount  of 
positive  electricity  was  developed  at  the  same  time  in  the 
flannel.  It  is  as  though  the  two  electricities  were  united 
in  these  several  substances  in  their  ordinary  condition  and 
were  torn  asunder  by  the  friction,  thus  producing  actual 
"  electric  separation." 

(#.)  If  it  be  desired  to  show  that  the  rubber  has  been  electrified, 
care  must  be  taken  not  to  handle  it  too  much.  For  example,  if  seal- 
ing-wax is  to  be  rubbed  with  a  piece  of  fur,  do  not  take  the  fur  in 
the  hand,  but  fasten  it  to  the  end  of  a  glass  rod  as  a  handle. 

(6.)  That  the  electricities  thus  simultaneously  developed  are  op- 
posite in  kind  and  equal  in  amount  may  be  shown  by  imparting 
the  electricity  of  the  rubber  and  the  electricity  of  the  thing  rubbed 
to  a  third  body,  which  will  then  show  no  electrification  at  all.  The 
equal  and  opposite  electricities  exactly  neutralize  each  other. 

317.  The  Two  Electricities  Named.— As  the 

two  kinds  of  electricity  are  opposite  in  character,  they 
have  received  names  that  indicate  opposition.  The  elec- 
tricity developed  on  glass  by  rubbing  it  with  silk 


ELECTRICITY.  195 


is  called  positive  or  +.  The  electricity  developed 
on  sealing-wax  by  rubbing  it  with  flannel  is  called 
negative  or  —  .  The  terms  vitreous  and  resinous 
respectively  were  formerly  used. 

318.  Electric  Series.—  In  the  following  list,  the  substances 
are  named  in  such  an  order  that,  if  any  two  be  rubbed  together,  the 
one  that  stands  earlier  in  the  series  becomes  positively  electrified 
and  the  one  that  is  mentioned  later  becomes  negatively  electrified  : 
fur,  wool,  resin,  glass,  silk,  metals,  sulphur,  india-rubber,  gutta  percha, 
collodion. 

319.  The  Laws  of  Electrostatics.—  The  most 
important  electrostatic  laws  may  be  stated  thus  : 

(1.)  Electric  charges  of  like  signs  repel  each  other  ; 
electric  charges  of  opposite  signs  attract 
each  other. 

(2.  )  The  force  exerted  between  two  electric  charges 
is  directly  proportional  to  their  product 
and  inversely  proportional  to  the  square 
of  the  distance  between  them.  This  is  known 
as  Coulomb's  law.  The  two  charges  are  sup- 
posed to  be  collected  at  two  points,  or  on  two 

very  small  spheres.    /  =  —&    - 

(a.)  Suppose  that  a  and  6  are  two  small  balls,  each  charged  with 
a  quantity  of  electricity,  that  we  shall  call  unity.  Then  the  product 
of  the  charges  will  be  1  xl=l.  Next,  suppose  that  A  and  B  are 
two  similar  balls,  that  A  is  charged  with  twice  as  much  electricity  as 
a  and  that,  similarly,  B  has  a  charge  represented  by  3.  The  prod- 
uct of  the  charges  of  A  and  B  will  be  2  x  3=6.  In  other  words,  at 
equal  distances,  the  repulsion  between  A  and  B  will  be  six  times  as 
great  as  the  repulsion  between  a  and  b. 

(b.)  Suppose  that  two  electric  charges  or  two  small  electrified 
bodies  one  inch  apart  repel  each  other  with  a  certain  force  ;  at  a  dis- 
tance of  two  inches,  they  will  repel  each  other  with  a  force  one  quarter 
as  great  ;  at  a  distance  of  ten  inches,  they  will  repel  each  other  with 
only  one  per  cent,  of  the  original  force  at  the  distance  of  one  inch. 


190  FRICT10NAL  ELECTRICITY. 

320.  Electrical  Units. — There  are  two  systems  of 
electrical  units  derived  from  the  fundamental  "C.G-.S." 
units,  one  set  being  based  upon  the  attraction  or  repulsion 
exerted    between    two  quantities  of  electricity  and  the 
other  upon  the  force  exerted  between  two  magnefc  poles. 
The  former  are  termed  electrostatic  units ;  the  latter,  elec- 
tromagnetic units. 

321.  Electrostatic   Unit   of  Quantity.— One 

unit  of  electricity  is  that  quantity  ivhich,  when 
placed,  at  a  distance  of  one  centimeter  from  a 
similar  and  equal  quantity,  repels  it  with  a  force 
of  one  dyne.  It  is  a  C.G.S.  unit  (§  69)  and  has  no 
special  name. 

(a.)  Two  small  spheres,  charged  respectively  with  6  units  and  8 
units  of  +  electricity,  are  placed  4  cm.  aoart ;  find  what  force  they 
exert  on  one  another. 

By  the  formula,  /  =  Sli,  we  find  /  =  ll§  =  *§  =  3. 

Ans.  3  dynes. 

The  force  in  the  above  example  would  clearly  be  a  force  of  repul- 
sion. Had  one  of  these  charges  been  negative,  the  product,  Q  x  g, 
would  have  had  a  —  value  (algebraic)  and  the  answer  would  have 
been  minus  3  dynes.  The  algebraic  —  sign,  therefore,  prefixed  to 
a  force,  indicates  that  it  is  a  force  of  attraction,  while  the  +  sign 
signifies  a  force  of  repulsion. 

322.  The   Test   for  Either  Kind   of  Elec- 
tricity.— When  the  pith  ball  was  attracted  by  the  rubbed 
glass  it  became,  during  the  time  of  contact,  charged  with 
the  +  electricity  of  the  glass;    hence  it  was  repelled. 
When  it  was  attracted  by  the  rubbed  sealing-wax  it  be- 
came, during  the  time  of  contact,  charged  with  the  — 
electricity  of  the  wax ;  then  it  was  repelled.     But  either 


FRICTIONAL   ELECTRICITY, 


197 


the  wax  or  the  glass  attracted  the  uncharged  pith  ball. 
We  must,  therefore,  remember  that  attraction  affords 
no  safe  test  for  the  kind  of  electricity,  while  re- 
pulsion does.  If  glass  rubbed  with  silk  repels  a  body, 
that  body  is  charged  with  -f-  electricity.  If  sealing-wax 
rubbed  with  flannel  repels  a  body,  that  body  is  charged 
with  —  electricity. 

323.  Electroscopes. — An  instrument  used  to 
detect  the  presence  of  electricity,  or  to  determine 
its  kind,  is  called  an  electroscope.  The  electric  pen- 
dulum (§  304)  is  a  common  form  of  the  electroscope. 
Two  strips  of  the  thinnest  tissue  paper  hanging  side  by 
side  constitute  a  simple  electroscope.  It  is  well  to  prepare 
the  paper  beforehand  by  soaking  in  a  strong  solution  of 
salt  in  water  and  drying. 
The  balanced  straw  (Fig. 
119)  or,  better  yet,  two 
gilded  pith  balls  connected 
by  a  light  needle  of  glass 
or  sealing-wax  balanced 
horizontally  on  a  vertical 
pivot,  or  a  goose-quill 
balanced  on  the  point  of 
a  sewing-needle,  makes  i? 
convenient  electroscope. 

The  gold  leaf  electro- 
scope is  represented  in 
Fig.  129.  A  metallic  rod,  which  passes  through  the  cork 
of  a  glass  vessel,  terminates  below  in  two  narrow  strips  of 
gold  leaf  and  above  in  a  metallic  knob  or  plate.  The 
object  of  the  vessel  is  to  protect  the  leaves  from  disturb- 
ance by  air  currents.  The  upper  part  of  the  glass  is  often 


FIG.  129. 


193  FRICTION AL  ELECTRICITY. 

coated  with  a  solution  of  sealing-wax  or  shellac  in  alcohol, 
to  lessen  the  deposition  of  moisture  from  the  atmosphere. 
This  instrument  may  be  made  by  the  pupil  and,  when 
well  made,  is  very  delicate. 

(a.)  The  electric  pendulum  is  used  as  an  electroscope  as  follows 
If  an  uncharged  pith  ball  be  attracted  by  a  body  brought  near  it, 
the  body  is  electrified.  To  determine  the  sign  of  the  electricity  of 
the  body  thus  shown  to  be  electrified,  the  pith  ball  is  allowed  to 
touch  it  and  be  repelled.  If  the  ball  then  be  repelled  by  a  glass  rod 
rubbed  with  silk  (or  by  any  other  body  known  to  be  positively 
charged),  the  pith  ball  and  the  body  in  question  manifest  -f  elec 
tricity.  If  the  pith  ball,  after  repulsion  by  the  body  whose  elec- 
tricity is  under  examination,  be  repelled  by  sealing-wax  rubbed  with 
flannel  (or  by  any  other  body  known  to  be  negatively  charged),  the 
pith  ball  and  the  body  in  question  manifest  —  electricity.  Remem- 
ber that  the  repulsion  and  not  the  attraction  constitutes  the  test. 

(&.)  One  way  of  testing  with  the  gold  leaf  electroscope  is  to  bring 
the  electrified  body  near  the  knob ;  the  leaves  will  diverge.  Touch 
the  knob  with  the  finger ;  the  leaves  will  fall  together.  Remove  first 
the  finger  and  then  the  electrified  body  ;  the  leaves  will  diverge 
again.  If  now  the  divergence  of  the  leaves  be  increased  by  bring- 
ing a  positively  charged  body  near  the  knob,  the  original  charge 
was  —  ;  if  the  divergence  be  thus  diminished,  the  original  charge 
was  +. 

(c.)  The  knob  and  rod  of  the  gold  leaf  electroscope  may  be  made 
by  soldering  a  wire  to  a  smooth  metal  button.  The  vessel  may  be 
any  clear  glass  bottle  with  a  wide  mouth.  Thrust  the  wire  down- 
ward through  the  cork  of  the  bottle  and  bend  the  wire  at  right 
angles,  so  that  when  the  cork  is  in  place  the  horizontal  part  of  the 
wire  shall  be  about  f  inch  long  and  come  just  below  the  shoulder  of 
the  bottle.  Cut  a  strip  of  gold  or  Dutch  leaf,  4  inches  long  and  ^ 
inch  wide  and  paste  it  at  its  middle  line  to  the  horizontal  part  of  the 
wire,  so  that  the  two  halves  of  the  strip  shall  hang  downward  facing 
each  other.  See  that  the  cork  is  perfectly  dry  ;  heat  the  bottle  until 
it  is  perfectly  dry ;  insert  the  cork  firmly  in  its  place,  and  pour 
melted  sealing-wax  over  the  cork  and  around  the  mouth  of  the 
bottle  so  that  no  moisture  can  get  into  your  electroscope.  If  you 
cannot  get  the  gold  or  Dutch  leaf  (try  at  some  good-natured  dentist's 
or  sign  painter's),  use  two  discs  of  gilt  paper  as  large  as  the  mouth 
of  your  bottle  will  admit  and  tie  them  to  the  wire  by  very  short 
cottoo  or  linen  threads.. 


FRICTIONAL   ELECTRICITY. 


199 


Experiment  23. — From  a  horizontal  glass  rod  or  tightly-stretched 
•ilk  cord,  suspend  a  fine  copper  wire,  a  linen  thread  and  two  silk 
threads,  each  at  least  a  meter  long.  To  the  lower  end  of  each,  at- 
tach a  metal  weight  of  any  kind.  Place  the  weight  supported  by 
the  wire  upon  the  plate  of  the  gold  leaf  electroscope.  Bring  the 
electrified  glass  rod  near  the  upper  end  of  the  wire  ;  the  gold  leaves 
instantly  diverge.  Repeat  the  experiment  with  the  linen  thread  ;  in 
a  little  while  the  leaves  diverge.  Repeat  the  experiment  with  the 
dry  silk  thread  ;  the  leaves  do  not  diverge  at  all.  Rub  the  rod  upon 
the  upper  end  of  the  silk  thread ;  no  divergence  yet  appears.  Wet 
the  second  silk  cord  thoroughly  and,  with  it,  repeat  the  experiment  ; 
the  leaves  then  diverge  instantly. 

Experiment  24.— Support  a  yard  stick  or  common  lath  upon  a 
glass  tumbler.  Bring  the  glass  rod,  electrified  by  rubbing  it  with 
silk,  to  one  end  of  the  stick  and  hold  some  small  pieces  of  gold  leaf 
or  paper  under  the  other  end  of  the  stick.  The  gold  leaf  or  paper 
will  be  attracted  and  repelled  by  the  stick  as  it  previously  was  by 
the  glass  itself.  The  electricity  passed  along  the  stick  from  end  to  end. 

324:.  Conductors. — Such  experiments  clearly  show 
that  some  substances  transmit  electricity  readily  and 
that  others  do  not.  Those  that  offer  little  resistance 
to  the  passage  of  electricity  are  called  conductors ; 
those  that  offer  great  resistance  are  called  non- 
conductors or  insulators.  A  conductor  supported  by  a 
non-conductor  is  said  to  be  insulated. 

(a.)  In  the  following  table,  the  substances  named  are  arranged  in 
the  order  of  their  conductivity-: 


Conductors. 
t.  Metals. 
2.  Charcoal. 
3.  Graphite. 
4.  Acids. 

5.  Salt  water. 
6.  Fresh  water. 
7.  Vegetables. 
8.  Animals. 
9.  Linen. 

10.  Cotton. 
11.  Dry  wood. 
12.  Paper. 
13.  Silk. 
14.  India  rubber. 

15.  Porcelain. 
16.  Glass. 
17.  Sealing-wax. 
18.  Vulcanite. 
Insulators. 

(&.)  The  fact  that  a  conductor  in  the  air  may  be  insulated,  show?; 
that  air  is  a  non-conductor.  Dry  air  is  a  very  good  insulator  (at 
least  1026  times  as  good  as  copper),  but  moist  air  is  a  fairly  good 
conductor  for  electricity  of  high  potential.  All  experiments  in  fric- 
tional  electricity  should,  therefore,  be  performed  in  clear,  cold  weather 


200  FRICTIONAL  ELECTRICITY. 

when  the  atmosphere  is  dry,  for  a  moist  atmosphere  renders  insula 
tion  for  a  considerable  length  of  time  impossible. 

(c.)  A  simple  way  of  determining  experimentally  whether  a  body  is 
a  good  conductor  or  not  is,  to  hold  it  in  the  hand  and  touch  the  knob 
of  a  charged  gold  leaf  electroscope  with  it.  If  the  substance  be  a 
good  conductor,  the  electroscope  will  be  quickly  discharged. 

Experiment  25. — Suspend  a  copper  globe  or  other  metal  body  by 
a  silk  thread  and  strike  it  two  or  three  times  with  a  cat's  skin  or 
fox's  brush.  Bring  the  gold  leaf  electroscope  near  the  globe.  The 
leaves  will  diverge. 

325.  Electrics. — Any  substance,  when  insulated, 
inay  be  sensibly  electrified ;  but  when  an  uninsulated 
conductor  is  rubbed,  the  electricity  escapes  as  fast 
as  it  is  developed.    The  old  division  of  bodies  into  elec- 
trics and  non-electrics,  or  bodies  that  can  be  electrified 
and  those  that  cannot  be  electrified,  is  nothing  more  than 
a  division  into  conductors  and  non-conductors. 

326.  Tension. — Electricity  exists  under  widely  dif- 
ferent conditions  with  respect  to  its  ability  to  force  its 
way  through  a  poor  conductor  or  to  leap  across  a  gap. 
The  electricity  developed  Tn  a  voltaic  cell  will  not  pass 
through  even  a  very  thin  piece  of  dry  wood  ;   the  elec- 
tricity developed  by  rubbing  the  glass  rod  will  pass  through 
several  feet  of  dry  wood.    It  would  require  a  battery  of 
many  cells  to  force  a  current  across  an  air-filled  gap  of 
y^fl-  of  an  inch.     It  is  not  difficult  to  force  friction al 
electricity  across  a  gap  of  several  inches,  while  we  all  know 
that,  in  the  case  of  lightning,  electricity  leaps  across  a 
gap  of  many  hundred  feet.    In  the  one  case,  the  electricity 
is  said  to  be  of  low  potential ;  in  the  other  case,  it  is  said 
to  be  of  high  potential.     The  terms  "low  tension"  and 
"  high  tension  "  are  often  used  in  the  same  sense. 


FRICTIONAL   ELECTRICITY.  201 

327.  Potential. — The  term,  electrical  potential  (or 
simply  potential),  has  reference  to  the  electrical  condition 
of  a  body,  or  to  its  degree  of  electrification.    If  the  poten- 
tial of  A  be  higher  than  that  of  B  and  the  two  bodies  be 
connected   by  a  good   conductor,   an  electric  current 
will  flow  from   A    to    B   until    the   potentials    are 
alike.     Difference  of  potential  is  somewhat  analogous  to 
difference  of  liquid  level  and  gives  rise  to  electromotive 
force. 

(«.)  The  electric  condition  of  the  earth  is  sometimes  taken  as  the 
zero  of  potential.  The  electric  condition  of  other  bodies  is  then 
described  as  being  a  certain  number  of  units  above  or  below  zero  ; 
i.e.,  as  being  +  or  — .  In  determining  the  flow  of  liquids,  it  is  not 
necessary  to  know  the  height  of  either  reservoir  above  the  earth's 
centre  or  above  the  sea  level,  but  only  the  head  or  difference  of 
liquid  level.  Similarly,  the  difference  of  potential  is  what  determines 
the  direction  and  strength  of  an  electric  current  flowing  through  a 
given  conductor. 

328.  Difference  of  Potential.— The  difference 
of  potential  between  two  points  represents  the  work 
that  must  be  done  in  carrying  a  +  unit  of  electricity 
(§321)  from  one  point  to  the  other.     The  work  done 
will  be  the  same,  whatever  the  path  along  which  the  unit 
is  moved  from  one  point  to  the  other.     Similarly,   the 
work  done  in  lifting  a  weight  from  one  point  to  another 
at  a  higher  level  will  be  the  same  whatever  the  path  along 
which  the  weight  is  lifted. 

329.  Electrostatic   Unit   of  Difference    of 
Potential. — The  unit  of  difference  of  potential  is 
that  which  exists  between  two  points,  when   it  re- 
quires the  expenditure  of  one  erg  to  bring  a  unit 
of  -f-  electricity  from  one  point  to  another  against 


202  FRICTIONAL   ELECTRICITY. 

the  electric  force.     Let  A  be  a  small  sphere  positively 

electri6ed  and  P  and  §,  two  points  at  different  distances 

from    A.      If  Q  is   just   so   far 

,---"  from  P  that  it  requires  one  erg 

^       \  of  work   to   push  a  unit   of  -f 

electricity  from  Q  to  P,  there 
•  ?  t  will  be  unit  difference  of  poten- 
tial between  P  and  Q.  This 
unit  has  no  special  name. 

(a.)  Let   P  and   Q  be  in  the  outer 

FIG.   130.  surfaces  of  concentric,  spherical,  shells 

at  the  centre  of  which  is  A.    To  move 

the  +  unit  from  one  point  in  either  of  these  surfaces  to  any  other 
point  in  the  same  surface  requires  no  further  overcoming  of  elec- 
tric forces  and,  therefore,  no  expenditure  of  work.  Such  a  surface 
is  called  an  equipotential  surface. 

330.  Electric  Capacity.— Bodies  vary  in  respect 
to  their  capacity  for  holding  or  accumulating  electricity. 
The    electrostatic  unit  of  capacity  is  the  capacity 
of  a  conductor  that  requires  a  charge  of  one  unit 
of  electricity  to   raise   its  potential   from   zero    to 
unity.     It  has  no  special  name.     A  sphere  of  one  centi- 
meter radius  has  unit  capacity.     The  capacities  of  spheres 
are  proportional  to  their  radii.     (See  §  359.) 

(a.)  A  small  conductor  (e.g.,  a  sphere  the  size  of  a  pea)  will  require 
less  than  one  unit  to  raise  its  potential  from  0  to  1  ;  it  is  of  small 
capacity.  A  sphere  five  meters  in  diameter  will  require  many  units 
to  raise  its  potential  from  0  to  1  ;  it  is  of  preat  capacity.  In  other 
words,  the  electrostatic  capacity  of  a  conductor  or  condenser  is 
measured  by  the  quantity  of  electricity  which  must  be  imparted  to 
it  in  order  to  raise  its  potential  from  0  to  1. 

331.  Charging-  by  Contact.— If  an  insulated,  un- 
electrified  conductor  be  brought  into  contact  with  a  simi- 


FRICTIONAL   ELECTRICITY. 


203 


lar  conductor  that  is  electrified,  or  near  enough  to  it  for 
the  easy  passage  of  an  electric  spark,  electricity  will  pass 
from  the  latter  to  the  former  until  the  two  conductors  are 
equally  charged  with  the  same  kind  of  electricity,  i.e.,  un- 
til they  are  of  the  same  potential.  The  former  is  said 
to  be  charged  ~by  conduction. 

332.  Electrostatic  Induction.— From  several  of 
the  preceding  experiments,  we  see  that  actual  contact  with 
an  electrified  body  is 
not  necessary  for  the 
manifestation  of  electric 
action  in  an  unelectri- 
fied  body.  When  an 
electrified  body,  (7,  is 
brought  near  an  insu- 
lated, unelectrified  con- 
ductor, B,  provided 
with  electric  pendu- 
lums, as  shown  in  Fig.  131,  the  latter  shows  electric  ac- 
tion. The  electricity  of  C  repels  one  kind  of  electricity 
in  B  and  attracts  the  other,  thus  separating  them.  The 
second  body,  B,  is  then  said  to  be  polarized. 

The  two  kinds  of  electricity  in  B,  each  of  which  a  mo- 
ment ago  rendered  the  other  powerless,  are  still  there,  but 
they  have  been  separated  and  each  olothed  with  its  proper 
power.  This  effect  is  due  to  the  action  of  the  electrified 
body,  C,  which  is  said  to  produce  electric  separation  by 
induction.  This  action  will  take  place  across  a  consider- 
able distance,  even  if  a  large  sheet  of  glass  be  held  be- 
tween B  and  C.  When  C  is  removed,  the  separated  elec- 
tricities of  B  again  mingle  and  neutralize  each  other. 


FIG.  131. 


204 


FRICTIONAL  ELECTRICITY. 


(a.)  Conductors  for  the  purposes  of  this  and  similar  experiments 
may  be  made  of  wood,  covered  with  tin-foil,  gold  leaf  or  Dutch 
leaf.  They  may  be  insulated  by  fastening  them  on  top  of  long- 
necked  bottles  or  sticks  of  sealing-wax,  or  by  suspending  them  by 
silk  threads. 

(&.)  Prick  a  pin-hole  in  each  end  of  a  hen's  egg  and  blow  out  the 
contents  of  the  shell.  Paste  tin-foil  or  Dutch  leaf  smoothly  over 
the  whole  surface  of  the  egg.  Fasten  one  end  of  a  white  silk  thread 

to  the  egg  with  a  drop 
of  melted  sealing-wax, 
so  that  the  egg  may 
hang  suspended  with  its 
greater  diameter  hori- 
zontal. Three  or  four 
such  insulated  conduc- 
tors will  be  found  con- 
venient. Sometimes,  it 
is  better  for  each  egg  to 
have  two  thread  sup- 
FIG.  132.  ports.  Place  a  loop  or 

ring  at  the  free  end  of 

each  thread.  When  the  loops  are  placed  on  a  horizontal  rod  (e.g.,  a 
piece  of  glass  tubing),  the  greater  diameters  of  the  suspended  eggs 
should  lie  in  the  same  straight  line.  An  elongated  conductor  like 
AB  of  Fig.  133  may  be  made  by  hanging  two  or  three  egg  con- 
ductors, so  that  they  are  in  contact,  as  shown  in  Fig.  132. 

Experiment  26. — While  the  charged  glass  rod  is  held  near  the 
egg  conductors,  shown  in  Fig.  132,  bring  a  pith  ball  electroscope 
near.  The  attraction  will  be  evident  at  the  free  ends  of  the  two 
eggs,  but  very  little,  if  any,  will  be  found  at  or  near  the  point 
where  the  eggs  are  in  contact. 

333.  A  Neutral  Line.— If  an  insulated  conductor, 
bearing  a  number  of  pith  ball  (or  paper)  electroscopes,  be 
brought  near  an  electrified  body,  (7,  (Fig.  133),  but  not 
near  enough  for  a  spark  to  pass  between  them,  the  pith 
balls  near  the  ends  of  the  conductor  will  diverge,  showing 
the  presence  of  separated  or  un combined  electricity.  The 
pith  balls  at  the  middle  of  the  polarized  conductor  will  not 
diverge,  marking  thus  a  neutral  line.  If  0  has  a  positive 


FRICTION AL  ELECTRICITY.  205 

charge,  the  charge  at  A  will  be  negative  and  that  at  B 
will  be  positive,  as  may  be  shown  by  charging  an  electric 
pendulum  and  testing  at  A  and  B. 


FIG.  133. 

If  0  be  removed  or  "  discharged  "  by  touching  it  with 
the  hand,  all  traces  of  electrical  separation  in  A  B  will 
disappear.  The  charged  pith  ball  will  be  attracted  at 
every  point  of  A  B. 

Experiment  27.— While  the  charged  glass  rod  is  held  near  the 
egg  conductors  shown  in  Fig.  133,  slide  the  loop,  carrying  A  about 
4  inches  (10  cm.}  to  the  left  and  then  hold  the  rod  between  the  two 
eggs.  The  rod  will  repel  one  egg  and  attract  the  other. 

334.  Charging  a  Body  by  Induction.— If  the 

polarized  conductor  be  touched  with  the  hand,  or  other- 
wise placed  in  electric  communication  with  the  earth,  the 
electricity  repelled  by  C  (Fig.  133)  will  escape,  and  the 
pith  balls  at  B  will  fall  together.  The  electricity  at  the 
other  end  will  be  held  by  the  mutual  attraction  between 
it  and  its  opposite  kind  at  G.  The  line  of  communica- 
tion with  the  ground  being  broken  and  the  conductor 


206  FR1CTIONAL  ELECTRICITY. 

being  removed  from  the  vicinity  of  O,  it  will  be  found 
charged  with  electricity  opposite  in  kind  to  that  of  C. 

A  body  may  be  thus  charged  by  induction  with 
no  loss  to  the  inducing  body.  If  the  conductor,  A  B, 
be  made  in  two  parts  and  the  parts  separated,  while 
under  the  inductive  action  of  the  electrified  body,  C9  the 
two  electricities  can  no  longer  return  to  neutralize  each 
other,  but  must  remain,  each  on  its  own  portion  of  the 
conductor.  The  two  parts  will  thus  be  oppositely  charged. 

335.  Successive  Induction. — If  a  series  of  insu- 
lated conductors,  like  the  egg  shells  of  Fig.  132,  be  placed 
in  line  as  shown  in  Fig.  134,  and  a  positively  electrified 


FIG.  134. 

body  be  brought  near,  each  conductor  will  be  polarized. 
The  first  will  be  polarized  by  the  influence  of  the  +  of 
(7;  the  second  by  the  influence  of  the  +  of  M,  and  so  on. 

(a.)  Either  kind  of  electricity  may  be  carried  from  M  or  N  by  a 
small  insulated  body,  called  a  proof-plane  (Fig.  139),  to  the  elec- 
troscope, there  tested  and  found  to  be  as  represented  in  the  figure. 
If  the  conductors,  M  and  N,  be  now  placed  in  actual  contact,  the  + 
of  both  will  be  repelled  by  G  to  the  furthest  extremity  of  N  and 
the  —  of  both  will  be  attracted  to  the  opposite  end  of  M,  near  to  Cl 


FRICTIONAL   ELECTRICITY.  207 

'&.)  It  is  very  plain  that  any  body  may  be  looked  upon  as  a  collet- 
lion  of  many  parallel  series  of  such  conductors,  each  molecule  rep- 
resenting a  conductor.  Thus,  each  molecule  may  be  polarized,  + 
at  one  end  and  —  at  the  other.  If  the  body  in  question  be  a  good 
conductor  of  electricity,  this  polarization  of  the  molecules  is  only  for 
an  instant.  The  two  electricities  pass  from  molecule  to  molecule 
and  accumulate  at  opposite  ends  of  the  body.  The  body  is  then 
polarized,  bat  not  the  molecules  of  the  body.  On  the  other  hand, 
good  insulators  resist  this  tendency  to  transmit  the  electricities  from 
molecule  to  molecule  and  are  able  to  maintain  a  high  degree  of 
molecular  polarization  for  a  great  length  of  time.  In  brief,  the 
molecules  of  conductors  easily  discharge  their  electricities  into  each 
other  ;  those  of  non-conductors  do  not. 

336.  Polarization    Precedes    Attraction. — 

When  an  electrified  glass  rod  is  brought  near  an  electric 
pendulum,  the  pith  ball  is  polarized 
as  shown  in  the  figure.     As  the  — 
electricity  of  the  ball  is  nearer  the  + 
of  the  glass  than  is  the  +  of  the  ball, 

the  attraction  is  greater  than  the  re- 

FIG.  135. 

pulsion.      If  the    pith   ball   be   sus- 
pended, not  by  a  silk  thread  but  by  some  good  conductor, 
the  attraction  will  be  more  marked,  for  the   -f-  of  the  ball 
will  escape  to  the  earth  through  the  support  and,  thus,  the 
repelling  component  will  be  removed. 

Note. — Polarization  and  electrification  by  induction  explain  a  great 
many  electrical  phenomena. 

337.  Provisional    Theory   of  Electricity.— 

While  the  real  nature  of  electricity  remains  unknown,  the 
following  theory  will  be  found  convenient  for  classifying 
results  already  attained  and  suggesting  directions  for  fur- 
ther inquiry.  But  we  must  not  let  it  influence  our  judg- 
ment as  to  what  is  the  true  and  full  explanation  of  elec- 


208  FRICTIONAL  ELECTRICITY. 

trical  phenomena,  which  explanation  may  be  found  here- 
after : 

(1.)  We  may  assume  that  a  neutral  or  unelectri- 
fied  body  contains  equal  and  equally  dis- 
tributed quantities  of  positive  and  of  nega- 
tive electricity. 

(2.)  We  may  assume  these  electricities  to  be  un- 
limited in  amount. 

(3.)  We  shall  then  conceive  that  a  positively  elec- 
trified body  has  an  excess  of  -f  electricity 
and  that  a  negatively  electrified  body  has 
an  excess  of  —  electricity. 

(4.)  In  this  light,  we  shall  see  that  communi- 
cating 4-  electricity  to  a  body  is  equiva- 
lent to  removing  an  equal  amount  of  — 
electricity  from  it,  and  conversely. 

338.  The  Electrophorus.— This  simple  instru- 
ment consists  generally  of  a  shallow  tinned  pan  filled  with 
resin,  on  which  rests  a  movable  metallic  cover  with  a  glass 
or  other  insulating  handle.  The  resinous  plate  may  be 
replaced  by  a  piece  of  vulcanized  india-rubber.  The  metal 
surface  and  the  resinous  surface  touch  at  only  a  few 
points ;  they  are  practically  separated  by  a  thin  layer  of 
insulating  air. 

(a.)  The  resinous  plate  may  be  prepared  by  melting  together 
equal  quantities  of  resin  and  Venice  turpentine  and  then  adding  a 
like  quantity  of  shellac.  The  substances  should  be  heated  gradually 
and  stirred  together  so  as  to  prevent  the  forming  of  bubbles.  Be 
careful  that  the  mixture  does  not  take  fire  in  course  of  preparation. 
The  Venice  turpentine  is  desirable,  but  not  necessary.  For  a  handle, 
a  stout  wire  may  be  soldered  to  the  centre  of  the  disc  and  covered 
with  rubber  tubing,  or  a  piece  of  sealing  wax,  of  convenient  size, 


FRICTIONAL  ELECTRICITY. 


209 


m 

FIG.  136. 


may  be  fastened  to  the  disc  for  the  purpose.  A  still  better  plan  is 
to  make  the  cover  of  wood,  a  little  less  in  diameter  than  the  resinous 
plate.  Its  edges  should  be  carefully  rounded  off.  For  a  handle,  a 
glass  rod  or  tube  may  be  tightly 
thrust  or  cemented  into  a  hole  in 
the  middle  of  the  cover.  Place  tin- 
foil all  over  the  cover  and  smooth 
down  all  rough  ed^es  of  the  foil 
with  the  finger-nail  or  paper-folder. 
The  wire  support  for  a  pith  ball  or 
paper  electroscope  may  be  thrust 
into  the  wood  of  the  cover,  care  be- 
ing taken  that  it  touches  the  tin- 
foil. 

(&.)  For  an  electroscope  for  the 
electro phorus,  provide  a  bit  of  wire 
about  8  cm.  long  and  bend  it  at 
right  angles  about  1  cm.  from,  each 
end.  Solder  one  of  the  bent  arms 
of  the  wire  (see  Appendix  B)  to 
the  upper  side  of  the  metal  cover,  near  its  edge,  in  such  a  way  that 
the  central  part  of  the  wire  shall  be  vertical.  Cut  a  strip  of  gold 
leaf  (or  Dutch  metal)  about  8  cm.  long  and  8  mm.  wide.  Moisten 
the  sides  of  the  free  horizontal  wire-arm  with  a  little  mucilage, 
place  the  middle  of  the  gold-leaf  strip  over  the  top  of  the  arm  and 
bring  the  ends  of  the  leaf  down  to  a  vertical  position,  touching  each 
other.  The  mucilage  will  hold  the  leaf  to  the  wire.  When  the 
wire  support  and  gold  leaves  are  electrified,  the  latter  will  diverge. 
When  the  apparatus  is  not  in  use,  this  electroscope  may  be  protected 
by  inverting  a  tumbler  or  beaker  glass  over  it. 

(c.)  The  plate  is  rubbed  or  struck  with  flannel  or  catskin  and 
thus  negatively  electrified.  The  cover  is  then  placed  upon  the  resin 
and  thus  polarized  by  induction.  If  the  cover  be  provided  with  a 
gold-leaf  electroscope,  the  free  negative  electricity  of  the  cover  will 
cause  the  leaves  to  diverge  ;  the  positive  electricity  of  the  cover 
will  be  "  bound "  on  the  under  side  of  the  cover  by  the  attraction 
of  the  negative  electricity  of  the  resin.  Remove  the  cover  and  the 
separated  electricities  reunite,  as  is  shown  by  the  falling  together  of 
the  lately  divergent  gold  leaves.  Place  the  cover  again  upon  the 
resin.  Polarization  is  manifested  by  the  divergence  of  the  leaves. 
Touch  the  cover  with  the  finger  as  shown  in  the  figure ;  the  — 
electricity  escapes  and  the  leaves  fall.  The  cover  is  now  charged 
positively,  but  its  electricity  is  all  "bound"  at  Us  under  surface 


210 


FR1CTIONAL   ELECTRICITY. 


and  cannot  cause  the  leaves  to  separate.  Remove  the  cover  by  its 
insulating  handle  and  the  electricity,  lately  "bound"  but  now 
"  free,"  diffuses  itself  and  the  leaves  are  divergent  with  +  elec- 
tricity. The  charged  cover  will  give  a  spark  to  the  knuckle  or  other 
unelectrified  body  presented  to  it.  (Fig.  137.) 


339.  The  Electrophorus  Charged  by  Induc- 
tion.— The  cover  may 
be  thus  charged  and 
discharged  an  indefi- 
nite number  of  times, 
in  favorable  weather, 
without  a  second  elec- 
trifying of  the  resinous 
plate.  This  could  not 
happen  if  the  electricity 
of  the  cover  were  drawn 
from  the  plate.  More- 
over, if  the  charge  of 
the  cover  were  drawn 
from  the  plate,  it  would 
be  — ,  and  not  +  . 
There  is  no  escape  from 
the  conclusion  that  the 


FIG.  137. 
cover  is  charged  by  induction  and  not  by  conduction. 


(a.)  If  the  resin  were  a  good  conductor  like  the  metal  cover,  its 
molecules  would  all  receive  +  electricity  from  the  cover  and  give 
—  electricity  to  it.  But  as  the  resin  is  a  poor  conductor,  only  the 
very  few  molecules  that  come  in  actual  contact  with  the  cover  at 
each  charging  Lave  their  electrical  equilibrium  restored.  The  + 
of  the  cover  cannot  readily  pass  through  them  to  their  electrified 
neighbors.  Hence,  it  requires  a  great  many  placings  of  the  cover 
upon  the  plate  to  discharge  the  resin  by  reconveying  to  it  the  + 
electricity  removed  at  its  electrification.  When  the  cover  is  charged, 
it  gives  up  part  of  its  —  electricity ;  when  it  is  discharged,  it  re- 


FRACTIONAL   ELECTRICITY. 


211 


ceives  this  —  electricity  back  again  from  the  body  that  discharges 
it.  As  this  giving  and  taking  is  neither  to  nor  from  the  resin,  it 
may  be  continued  almost  indefinitely.  A  Leyden  jar  (§  353)  may  be 
charged  with  an  electrophorus. 

34O.  Whence  this  Energy  ? — At  every  discharge 
of  the  electrophorus,  it  gives  a  definite  amount  of  elec- 
tricity, capable  of  doing  a  definite  amount  of  work.  As 
this  is  obtained  not  by  the  expenditure  of  any  part  of  the 
original  charge,,  we  are  led  to  seek  for  the  source  of  this 
apparently  unlimited  supply  of  energy. 

"  As  a  matter  of  fact,  it  is  a  little  harder  work  to  lift 
the  cover  when  it  is  charged  with  the  +  electricity  than 
if  it  were  not  charged,  for,  when  charged,  there  is  the 


FIG.  138. 

;orce  of  electric  attraction  to  be  overcome  as  well  as  the 
force  of  gravity.  Slightly  harder  work  is  done  at  the  ex- 
pense of  the  muscular  energies  of  the  operator  and  this  is 


212 


FRICTIONAL  ELECTRICITY. 


the  real  origin  of  the  energy  stored  up  in  the  separate 
charges." 

Experiment  28. — Insulate  a  metal  globe  and  provide  it  with  two 
closely  fitting  hemispherical  shells  that  have  insulating  handles. 
Electrify  the  globe  ;  bring  it  near  the  electroscope  to  be  sure  that  it  is 
electrified.  Place  the  hemispheres  upon  the  globe.  Remove  them 
quickly,  being  careful  that  their  edges  do  not  touch  the  sphere 
after  the  first  separation.  (Fig.  138.)  Bring  first  one  shell  and  then 
the  other  near  the  electroscope ;  they  are  electrified.  Bring  the  globe 
itself  near  the  electroscope.  It  is  no  longer  electrified.  Delicate 
manipulation  is  needed  to  make  the  experiment  successful.  You 
will  fail,  perhaps,  more  times  than  you  succeed.  But  when  the 
experiment  is  successful,  it  is  instructive.  The  apparatus  is  called 
Biot's  hemispheres. 


FIG.  139. 

Experiment  29.— By  means  of  a  few  sparks  rroir  tne  elect:* 
phorus,  charge  an  insulated  hollow  sphere,  li&vai%  an  orifice  in  tlae 


FRICTION AL  ELECTRICITY. 


213 


top.  Bring  a  proof  plane  (made  by  fastening  a  disc  of  gilt  paper  to 
a  long,  thin  insulating  handle)  into  contact  with  the  outer  surface 
of  the  sphere.  The  proof-plane  is  charged  by  the  sphere,  as  may  be 
shown  by  bringing  it  near -an  electroscope.  Discharge  the  proof 
plane  and  bring  it  into  contact  with  the  inner  surface  of  the  sphere. 
Remove  it  carefully  without  allowing  it  to  touch  the  sides  of  the 
orifice.  Bring  it  to  the  electroscope.  It  is  not  charged.  (Fig.  139.) 
An  empty  tin  fruit  can  supported  on  a  clean,  dry,  glass  tumbler  will 
answer  for  the  experiment. 


Experiment  30.— Make  a  conical  bag 
of  linen,  supported,  as  shown  in  Fig. 
140,  by  an  insulated  metal  hoop  five  or 
six  inches  in  diameter.  Charge  the  bag 
with  the  electrophorus.  A  long  silk 
thread  extending  each  way  from  the 
apex  of  the  cone  will  enable  you  to  turn 
the  bag  inside  out  without  discharging 
it.  Test  the  inside  and  outside  of  the 
bag,  using  the  proof-plane  described 
above.  Turn  the  bag  and  repeat  the 
test.  Whichever  surface  of  the  linen  is 
external,  no  electricity  can  be  found  upon 
the  inside  of  the  bag.  Nothing  can  be 
more  conclusive  than  this. 


FIG.  140. 


Experiment  31. — Vary  the  experiment  by  the  use  of  a  hat  sus- 
pended by  silk  threads.  Notice  that  the  greatest  charge  can  be 
obtained  from  the  edges ;  less  from  the  curved  or  flat  surface ;  none 
from  the  inside. 


341.  A  Charge  Resides  on  the   Surface. — 

Many  experiments  have  been  made  showing  that  when  a 
conductor  is  electrified,  the  electricity  passes  to  the 
surface  and  escapes  if  the  body  be  not  insulated. 
A  bomb-shell  and  a  cannon  ball  of  equal  diameter  will 
receive  equal  quantities  of  electricity  from  the  same  source. 
The  hollow  conductors  commonly  used  in  experiments  with 
static  electricity  are  as  serviceable  as  if  they  were  solid. 
A  wooden  prime  conductor  coated  with  gold-leaf  is  as 


214  FRICTIONAL  ELECTRICITY. 

efficient  as  if  it  were  made  of  solid  gold.  Experiment  is 
unable  to  find  any  difference  in  this  respect  between  a 
solid  sphere  of  metal  and  the  thinnest  soap-bubble  of  the 
same  diameter. 

(«.)  This  does  not  apply  to  an  electric  current.  A  hollow  wm 
will  not  conduct  electricity  as  well  as  a  solid  wire  of  the  same 
diameter.  Electricity  may  be  drawn  to  the  inside  of  a  hollow  con- 
ductor by  placing  there  an  electrified,  insulated  body. 

(6.)  The  linen  bag  of  Experiment  30  was  devised  by  Michael 
Faraday,  but  his  most  striking  experiment  was  made  with  a  wooden 
cage,  measuring  12  feet  each  way,  covered  with  tin-foil,  insulated 
and  charged  by  a  powerful  electric  machine.  He  carried  his  most 
delicate  electroscopes  into  this  cage.  Large  sparks  and  brushes 
were  darting  off  from  every  part  of  the  outer  surface,  but  the  phil- 
osopher and  his  sensitive  instruments  within  the  cage  failed  to 
detect  the  least  electric  influence. 

Experiment  32. — Place  a  carrot  horizontally  upon  an  insulating 
support.  Into  one  end  of  the  carrot,  stick  a  sewing-needle.  Bring 
tne  electrified  glass  rod  near  the  point  of  the  needle  without  touching 
it.  The  —  electricity  of  the  carrot  quietly  escapes  from  the  point 
to  the  rod  and  the  carrot  is  charged  with  the  +  electricity  that 
remains. 


342.  Density. — Experiments  show  that  when  a  spher 
ical  conductor  is  charged,  the  electricity  is  evenly  dia 
tributed  over  the  surface,  provided  no  other  electrified 
body  be  near  to  affect  the  distribution  by  induction.  The 
electric  density  (or  number  of  electrical  units  per  unit  ot 
area)  is  the  same  at  every  point.  Experiments  on  an 
elongated  cylinder,  like  the  prime  conductor  of  the  elec- 
tric machine,  show  that  the  density  is  greater  at  the  ends. 
On  an  egg-shaped  conductor,  like  that  shown  in  Fig.  141, 
the  density  is  greatest  at  the  smaller  end.  In  general, 
the  electric  density  is  very  great  at  any  pointed 
part  of  a  charged  conductor. 


FRICTION AL   ELECTRICITY.  215 

This  density  at  a  point  may  become  so  great  that  the 
electricity  will  escape  rapidly  and  quietly,  the  air  particles 


FIG.  141. 

quickly  carrying  off  the  charge  by  convection.  This 
explains  the  effect  of  pointed  conductors,  which  plays  so 
important  a  part  in  the  action  of  electric  machines.  This 
property  will  be  illustrated  in  several  of  the  experiments 
of  §  371.  It  is  fundamental  to  the  quiet  action  of  light- 
ning rods. 

343.  Electric    Machines. — Machines   have    been 
made  for  developing  larger  supplies  of  electricity  more 
easily  than  can  be  done  with  a  rod  of  glass  or  sealing-wax 
or  with  the  electrophorus.     Each  of  them  consists  of  one 
part  for  producing  the  electricity  and  another  part  for 
collecting  it. 

344.  The  Plate  Electric  Machine.— This  in- 
strument is  represented  in  Fig.  142.     It  consists  of  an  in- 
sulator (or  electric),  a  rubber,  a  negative  and  a  positive  or 
prime  conductor.    The  electric  is  a  glass  (or  ebonite)  plate, 
A,  generally  one,  two  or  three  feet  in  diameter.     This  plate 
has  an  axis,  B,  and  handle,  C,  and  is  supported  upon  two 
upright  columns.     The  rubber,  Z>,  is  made  of  two  cush- 


216  FRlCTlONAL   ELECTRICITY. 

ions  of  silk  or  leather,  covered  with  amalgam  (see  §  302,  a). 
They  press  upon  the  sides  of  the  plate  and  are  supported 


FIG.  142. 

from  the  negative  conductor,  with  which  they  are  in 
electric  connection.  The  negative  conductor,  JV,  is  sup- 
ported upon  an  insulating  column  and,  when  only  posi- 
tive electricity  is  desired,  is  placed  in  electrical  connection 
with  the  earth  hy  means  of  a  chain  or  wire,  W.  The 
prime  conductor,  P,  is  insulated.  One  end  of  the  prime 
conductor  terminates  in  two  arms,  P,  which  extend  one 
on  either  side  of  the  plate.  These  arms,  being  studded 
with  points  projecting  toward  the  plate,  are  called  combs. 
The  teeth  of  the  combs  do  not  quite  touch  the  plate.  A 
silk  bag,  S,  is  often  supported  so  as  to  enclose  the  lower 
part  of  the  plate.  All  parts  of  the  instrument  except  the 
teeth  of  the  combs  are  carefully  rounded  and  polished, 
sharp  points  and  edges  being  avoided  to  prevent  the  es- 
cape of  electricity  as  already  explained.  This  avoiding  of 
points  and  edges  is  to  be  regarded  in  all  apparatus  for  use 
with  electricity  of  high  potential. 


FRICTION AL   ELECTRICITY. 

(a.}  The  pupil  may  make  a  plate  machine  without  much  expense. 
A  glazier  will  cut  for  him  a  disc  of  place  glass,  possibly  from  a 
fragment  on  hand.  The  edges  of  this  disc  may  be  rounded  on  a  wet 
grindstone.  A  hole  may  be  bored  in  the  middle  with  a  round  file 
kept  moistened  with  a  solution  of  camphor  in  turpentine.  The  con- 
ductors, AT  and  P,  may  be  made  of  wood  covered  with  gold-foil  or 
Dutch  leaf  and  supported  on  pieces  of  stout  glass  tubing.  The 
prime  conductor  may  well  have  two  such  supports.  The  arms  may 
consist  of  two  stout  wires  thrust  into  the  end  of  a  prime  conductor, 
their  free  ends  being  provided  with  knobs  of  lead  or  other  metal. 
The  combs  may  be  made  by  soldering  pin  points  to  one  side  of  each 
arm.  See  that  the  gold-foil  makes  actual  contact  with  the  metal 
arms.  See  that  all  metal  parts  except  the  pin  points  are  polished 
smooth.  The  columns  that  support  the  plate  may  be  made  of  sea- 
soned wood.  The  part  of  the  handle  to  which  the  hand  is  app^ed 
may  be  made  of  glass  or  insulated  by  covering  it  with  rubbe;- 
tubing. 

345.  Operation  of  the  Plate  Machine. — The 

plate  is  turned  by  the  handle.  Electric  separation  is  pro- 
duced by  the  friction  of  the  rubbers.  The  -j-  electricity  of 
the  rubber  and  negative  conductor  passes  to  the  plate;  the 
—  electricity  of  the  plate  passes  to  the  rubber  and  negative 
conductor.  The  part  of  the  plate  thus  positively  charged 
passes  to  the  combs  of  the  prime  conductor.  The  +  of 
the  plate  acts  inductively  upon  the  prime  conductor,  polar- 
izes it,  repels  the  -f  and  attracts  the  —  electricities.  Some 
of  the  —  electricity  thus  attracted  streams  from  the  points 
of  the  combs  against  the  glass,  while  some  of  the  -f  elec- 
tricity of  the  glass  escapes  to  the  prime  conductor.  This 
neutralizes  that  part  of  the  plate,  or  restores  its  electric 
equilibrium,  and  leaves  the  prime  conductor  positively 
charged.  As  each  successive  part  of  the  plate  passes  the 
rubber,  it  gives  off  —  electricity  and  takes  an  equal 
amount  of  -f  ;  as  it  passes  between  the  combs  it  gives  off 
its  +  electricity  and  takes  an  equal  amount  of  — .  The 


218  FRICTIONAL   ELECTRICITY. 

rubber  and  negative  conductor  are  kept  in  equilibrium  by 
means  of  their  connection  with  the  earth,  "  the  common 
reservoir."  As  the  plate  revolves,  the  lower  part,  passing 
from  N  to  P,  is  positively  charged ;  the  upper  part,  pass- 
ing from  P  to  JV,  is  neutralized.  If  negative  electricity 
be  desired,  the  ground  connection  is  changed  from  N  to 
P  and  the  charge  taken  from  N. 

346.  The  Dielectric  Machine.— This  instru- 
ment is  represented  in  Fig.  143.  Two  plates  of  vulcanite 
(ebonite),  A  and  B,  overlap  each  other  without  touching 
and  revolve  in  opposite  directions.  The  upper  plate  is 
made  to  revolve  much  more  rapidly  than  the  lower  by 
means  of  the  pulleys  shown  at  the  right  of  the  figure. 
The  prime  conductor  and  the  axes  of  the  two  plates  are 
carried  by  two  insulating  pillars.  From  the  prime  con- 
ductor, a  comb  is  presented  to  the  upper  part  of  the  upper 
plate.  Another  comb  is  presented  to  that  part  of  A  which 
is  overlapped  by  the  upper  part  of  B.  This  comb  is  con- 
nected by  a  universal  joint  at  e  with  a  discharging  rod  and 
ball,  which  may  be  brought  near  the  end  of  the  prime 
conductor  or  turned  away  from  it.  The  rubbers  and  the 
lower  comb  are  to  be  in  electrical  communication  with 
the  earth.  The  general  arrangement  is  clearly  set  forth 
in  the  figure. 

347.  Operation  of  the  Dielectric  Machine.— 

The  plate,  B,  is  turned  directly  by  the  handle  and  the 
plate,  A,  indirectly  by  the  aid  of  the  pulley.  The  plate, 
J9,  is  negatively  electrified  by  friction  with  the  rubber 
and  thus  acts  by  induction  upon  the  lower  part  of  A, 
which  is  thus  polarized.  The  -f  of  this  part  of  A  is 


FRICTION AL   ELECTRICITY. 


219 


bound  by  the  attraction  of  the  -  -  of  B,  while  the  —  of 
A  is  repelled,  escapes  by  the  lower  comb  and  is  replaced 
by  +  from  the  earth 
through  the  lower 
comb  and  its  ground 
connection.  This  part 
of  A,  thus  positively 
charged,  is  soon  re- 
moved from  the  induc- 
ing body  and  the  -f 
charge,  bound  by  B,  is 
set  free.  It  then 
comes  to  the  upper 
comb,  polarizes  it  and 
the  prime  conductor 
and  exchanges  some  of 
its  own  +  for  an  equal 
amount  of  —  from  the 
prime  conductor.  This 
neutralizes  that  part  of  the  upper  plate  and  leaves  the 
prime  conductor  positively  charged.  As  each  successive 
part  of  A  passes  the  lower  comb,  it  gives  off  —  electricity 
and  takes  an  equal  amount  of  -f-  ;  as  it  passes  the  upper 
comb,  it  gives  off  -f-  electricity  and  receives  an  equal 
amount  of  — .  The  charge  of  B  is  continually  main- 
tained by  friction  with  the  rubber.  When  the  discharging 
rod  and  ball  are  brought  near  the  prime  conductor,  as 
shown  in  the  figure,  a  rapid  succession  of  spark's  is  pro- 
duced, owing  to  the  recombination  of  the  separated  elec- 
tricities. If  another  body  is  to  be  charged  from  the  prime 
conductor,  the  ball  and  rod  may  be  turned  aside.  The 
efficiency  of  this  machine  is  greater  than  that  of  the  plate 


FIG.  143. 


220 


FRICTIONAL   ELECTRICITY. 


or  cylinder  machine.  It  is  less  affected  by  atmospheric 
moisture  and  is  more  compact,  but  the  vulcanite  plates 
seem  to  deteriorate  with  use.  They  should  be  washed 
occasionally  with  ammonia  water  and  rubbed  with  paraf- 
fin oil.  Machines  of  similar  construction,  but  having 
glass  plates,  are  made. 

348.  The  Holtz  Electric  Machine.— This  in- 
strument is  represented  in  Fig.  144.    It  contains  two  thin, 

circular  plates  of 
glass,  the  larger 
of  which  is  held 
fast  by  two  fixed 
pillars.  The 
smaller  plate  re- 
volves rapidly 
very  near  it. 
There  are  two 
holes  in  the  fixed 
FlG-  X44-  plate  near  the 

extremities  of  its  horizontal  diameter.  To  the  sides  of 
these  openings  are  fastened  paper  bands  called  armatures. 
The  armatures  point  in  a  direction  opposite  to  that  in 
which  the  revolving  plate  moves.  Opposite  these  armatures 
and  separated  from  them  by  the  revolving  plate,  are  two 
metallic  combs,  connected  respectively  with  the  two  knobs 
and  Leyden  jars  shown  in  the  front  of  the  picture.  One  of 
these  knobs  is  carried  by  a  sliding  rod  so  that  their  distance 
apart  is  easily  adjusted.  When  this  machine  works  well,  it 
gives  results  superior  to  either  of  those  previously  mentioned. 
It  is,  however,  peculiarly  subject  to  atmospheric  conditions 
and  is  generally  considered  extremely  capricious. 


FRICTIONAL  ELECTRICITY.  221 

349.  Action  of  the  Holtz  Machine.— To  un- 
derstand the  action  of  this  machine  requires  careful  atten- 
tion. The  knobs  are  placed  in  contact  and  a  small  initial 
charge  is  given  to  one  of  the  armatures  by  some  charged 
body,  as  a  piece  of  vulcanite  or  a  glass  rod.  The  handle 
is  then  turned,  the  effort  necessary  to  keep  up  the  motion 
increasing  rapidly.  The  knobs  are  then  separated  and  a 
series  of  discharges  takes  place  between  them. 

(a.)  Suppose  a  small  +  charge  to  be  imparted  at  the  outset  to  the 
right  armature.  This  charge  acts  inductively  across  the  revolving 
plate  upon  the  metallic  comb,  repels  +  electricity  through  it  and 
leaves  the  points  negatively  electrified.  They  discharge  negatively 
electrified  air  upon  the  front  surface  of  the  movable  plate  ;  the  re- 
pelled +  charge  passes  through  the  brass  rods  and  balls  and  is  dis- 
charged through  the  left  comb  upon  the  front  side  of  the  movable 
disc.  Here  it  acts  inductively  upon  the  paper  armature,  causing 
that  part  of  it  which  is  opposite  itself  to  be  negatively  charged  and 
repelling  a  +  charge  into  its  farthest  part,  viz.,  into  the  armature. 
This,  being  bluntly  pointed,  slowly  discharges  a  +  charge  upon 
the  back  of  the  movable  plate.  When  the  plate  is  turned  round, 
this  +  charge  on  the  back  conies  over  from  the  left  to  the  right  side 
and,  when  it  gets  opposite  the  comb,  increases  the  inductive  effect 
of  the  already  existing  +  charge  on  the  armature  and,  therefore, 
repels  more  electricity  through  the  brass  rods  and  knobs  into  the 
left  comb.  Meantime  the  —  charge,  which  we  saw  had  been  in- 
duced in  the  left  armature,  has  in  turn  acted  on  the  left  comb,  caus- 
ing a  +  charge  to  be  discharged  by  the  points  upon  the  front  of  the 
plate  and,  drawing  electricity  through  the  brass  rods  and  knobs, 
has  made  the  right  comb  still  more  highly  — ,  increasing  the  dis- 
charge of  negatively  electrified  air  upon  the  front  of  the  plate, 
neutralizing  the  +  charge  which  is  being  conveyed  over  from  the 
left.  These  actions  result  in  causing  the  top  half  of  the  moving 
disc  to  be  positively  electrified  on  both  sides  and  the  bottom  half  of 
the  disc  to  be  negatively  electrified.  The  charges  on  the  front 
serve,  as  they  are  carried  round,  to  neutralize  the  electricities  let  off 
by  the  points  of  the  combs  while  the  charges  on  the  back,  induced 
respectively  in  the  neighborhood  of  each  of  the  armatures,  serve, 
when  the  rotation  of  the  plate  conveys  them  round,  to  increase  the 
inductive  influence  of  the  charge  on  the  other  armature,  Hence,  a 


FRL 


very  small  initial  chai 

being  reached  when  tLt  LJctJ  —  j  ___  LJ  ___  ____ 

that  the  loss  of  electricity  at  their  surface  equals  the  gain  by  con- 
vection and  induction. 

Note.  —  Other  forms  of  electric  machines  are  made.  One  of  the 
latest  of  these,  known  as  the  Toepler-Holtz,  is  very  compact  and 
efficient  and  remarkably  free  from  the  limitations  of  atmospheric 
conditions.  It  may  be  described  as  a  continuously  acting  electro- 
phorus  (§  227).  A  very  good  one  may  be  bought  for  $25  or  more. 
One  should  be  provided  for  the  school  in  some  way  if  possible.  Any 
electrical  machine  should  be  free  from  dust  and  perfectly  dry  when 
used.  It  should  be  warmer  than  the  atmosphere  of  the  room,  that 
it  may  not  condense  moisture  from  the  surrounding  air.  The  drier 
the  atmosphere,  the  better  will  be  the  action  of  the  machine. 

EXERCISES. 

1.  How  can  you  show  that  there  are  two  opposite  kinds  of  elec- 
tricity ? 

2.  How  would  you  test  the  kind  of  electricity  of  an  electrified 
body? 

3.  Quickly  pass  a  rubber  comb  through  the  hair  and  determine 
whether  the  electricity  of  the  comb  is  positive  or  negative. 

4.  Why  do  we  regard  the  two  electric  charges  produced  simul- 
taneously by  rubbing1  together  two   bodies  as  being  of  opposite 
kinds? 

5.  Why  is  it  desirable  that  a  glass  rod  used  for  electrification  be 
warmer  than  the  atmosphere  of  the  room  where  it  is  used? 

6.  Electrify  one  insulated  egg-she]  1  conductor  (§  332,  6).     Bring  it 
near  a  second  conductor  but  not  in  contact  with  it.     Touch  the 
second  egg-shell  with  the  finger,     (a.)  Experimentally,  determine 
whether  the  second  egg-shell  is  electrified  or  not.     (b.)  If  you  find 
that  it  is,  what  word  explains  the  method  of  charging?    (c.)  If  the 
second  egg-shell  is  charged,  will  its  potential  and  the  potential  of  the 
first  be  of  the  same  or  of  opposite  signs  ? 

7.  (a.}  In  §  323,  b,  it  is  directed  that  an  electrified  body  be  brought 
"  near"  the  knob  of  the  gold-leaf  electroscope.     Why  not  touch  the 
knob  with  the   charged  body?     (6.)  Why  do  not  the  gold  leaves 
diverge  immediately  after  touching  the  knob  with  the  finger  as  there 
directed?    (c  )  If  the  electrified  body  being  tested  had  a  +  charge, 
is  the  charge  of  the  gold  leaves  +  or  —  ?     Explain. 

8.  (a.)  What  is  a  proof-plane  ?    (6.)  An  electroscope?    (c.)  Describe 
one  kind,  of  electroscope,     (d.)  Another  kind. 


FRICTIONAL  ELECTRICITY. 

9.  (a.)  Define  electrics,   conductors  and  insulators.      (&.)  Explain 
electric  induction. 

10.  (a.)  If  a  metal  globe  suspended  by  a  silk  cord  be  brought  near 
the  prime  conductor  of  an  electric  machine  in  action,  feeble  sparks 
will  be  produced.     Explain.     (6.)  If  the  globe  be  held  in  the  hand, 
stronger  sparks  will  be  produced.     Explain. 

11.  Twist  some  tissue  paper  into  a  loose  roll  about  six  inches  long. 
Stick  a  pin  through  the  middle  of  the  roll  into  a  vertical  support. 
Present  an  electrified  rod  to  one  end  of  the  roll  and  thus  cause  the 
roll  to  turn  about  the  pin  as  an  axis.     Give  this  piece  of  scientific 
apparatus  an  appropriate  name. 

12.  (a.)  Prepare  two  wire  stirrups,  A  and  B,  like  those  shown  in 
Fig.  121  and  suspend  them  by  threads.     Electrify  two  glass  rods 
by  rubbing  them  with  silk  and  place  them  in  the  stirrups.     Bring 
A  near  B.    Notice  the  repulsion,    (b.)  Repeat  the  experiment  with 
two  sticks  of  sealing-wax  that  have  been  electrified  by  rubbing  with 
flannel.    Notice  the  repulsion,    (c.)  Place  an  electrified  glass  rod  in  A 
and  an  electrified  stick  of  sealing-wax  in  B.     Notice  the  attraction. 
Give  the  law  illustrated  by  these  experiments. 

13.  Two  small  balls  are  charged  respectively  with  +  24  and  —  8 
units  of  electricity.     With  what  force  will  they  attract  one  another 
when  placed  at  a  distance  of  4  centimeters  from  one  another  ? 

Ans.  12  dynes. 

14.  If  these  two  balls  are  then  made  to  touch  for  an  instant  and 
then  put  back  in  their  former  positions,  with  what  force  will  they 
act  on  each  other  ?  Ans.  Repulsion  of  4  dynes. 


224 


FRICTIONAL   ELECTRICITY. 


Experiment  33. — Hang  a  negatively  charged  pith  ball  inside  a 
dry  glass  bottle.  Bring  an  electrified  glass  rod  to  the  outer  side  of 
the  bottle.  The  pith  ball  will  rush  to  the  side  of  the  bottle  nearest 
the  rod  because  of  the  attraction  between  the  opposite  electricities. 

Experiment  34. — Paste  a  piece  of  tin-foil,  two  or  three  inches 
square,  on  the  middle  of  each  face  of  a  pane  of  glass.  Hold  a  finger 
on  one  of  the  metallic  coats  while  the  other  coat  is  held,  for  a  short 
time,  in  contact  with  the  prime  conductor  of  an  electric  machine  in 
operation.  Remove  the  pane  and  place  it  on  edge  without  touching 
both  coats  at  the  same  time.  Although  both  coats  are  oppositely 
charged  (§  384),  they  may  be  touched  in  succession  without  any 
shock.  When  both  are  touched  at  the  same  time,  the  shock  is 
greater  than  would  have  been  received  from  the  prime  conductor  by 
which  this  condenser  was  charged. 

35O.    Condensation     of    Electricity.  —  Two 

suspended  pith  balls  oppositely  charged  attract  one 
another  across  the  intervening  air.  They  attract  mu- 
tually even  when  a  plate  of  glass  is  held  between  them 

although    neither    the    balls 
c  nor  their  electric  charges  can 

pass  through  the  glass.  In 
the  case  of  the  pane  of 
glass  with  its  two  tin-foil 
coats,  or  in  the  similar  case 
of  two  metallic  plates,  A 
and  B,  separated  by  a  layer 
of  dry  air  or  other  non- 
conductor, (7,  as  shown  in 
Fig.  145,  the  two  charges 
are  "bound,"  each  by  the 
attraction  of  its  opposite 
on  the  other  side  of  the 
pane.  It  is  found  that  two  such  coats  may  be  charged 
much  more  strongly  than  either  one  could  be  if  the  oppo- 
site coat  were  wanting.  If  a  third  plate  like  JB,  but  hav~ 


\\ 


FIG.  145. 


FRICTIONAL  ELECTRICITY.  225 

ing  no  opposite  plate  like  A,  be  connected  with  B  by  a 
copper  wire  and  the  middle  of  the  wire  brought  into  con- 
tact with  the  prime  conductor,  nearly  the  whole  charge 
will  go  to  B  and  very  little  to  the  third  plate.  The  ca- 
pacity of  a  charged  conductor  is  greatly  increased 
by  bringing  it  near  a  second  charged  conductor 
oppositely  charged.  Its  capacity  being  thus  increased, 
a  greater  quantity  of  electricity  must  be  put  into  it  to 
raise  it  to  as  high  a  potential.  Such  a  method  of  increas- 
ing the  quantity  of  electricity  that  a  conductor  may  re- 
ceive without  raising  its  potential  is  called  the  condensa- 
tion or  accumulation  of  electricity. 

351.  Electric  Condensers. — An  apparatus  for 
collecting  a  large  quantity  of  electricity  at  a  moderate  po- 
tential, as  just  described,  is  called  an  electric  condenser. 


(a.)  Let  A  and  B,  Fig.  146, 
represent  two  insulated  metallic 
plates  about  six  inches  in  diam- 
eter, separated  by  C,  a  plate  of 
glass  somewhat  larger.  Let  each 
metallic  plate  have  an  electric 
pendulum,  a  and  b.  Remove  A 
and  connect  B  with  the  conductor 
of  the  electric  machine,  by  means 
of  the  wire,  x.  The  divergence  of 
b  shows  the  presence  of  free  electricity.  Connect  A  with  the 
ground  by  the  wire,  y,  and  place  it  in  position  as  represented.  By 
the  inductive  influence  of  B,  the  -  electricity  of  A  is  drawn  to  the 
surface,  n,  while  the  +  escapes  by  y.  But  this  -  electricity  at  n 
attracts  the  +  of  B  largely  to  the  surface  m  and  holds  it  there  as 
bound  electricity,  thus  increasing  the  electrical  density  at  that  sur- 
face. This  change  is  shown  by  less  divergence  of  b.  Consequently, 
B  can  receive  more  electricity  from  the  machine,  which  will,  in 
turn,  attract  more  -  electricity  to  n.  This  further  supply  will,  in 


226 


FRICTIONAL   ELECTRICITY. 


FIG.  147. 


turn,  bind  more  of  the  +  electricity  of  B  at  m.  In  this  way,  a  large 
quantity  of  +  electricity  may  be  accumulated  at  m  and  a  large 

quantity  of  —  at  n. 
This  accumulation  may 
thus  go  on  until  the 
potential  at  the  sur- 
face, p,  is  equal  to  that 
of  the  machine,  as  it 
was  when  A  was  ab- 
sent.  Interrupting 
communication  by  x 
and  y,  both  plates  are 
charged.  The  vertical 
pendulum,  a,  shows  no 
free  electricity,  the 
electricity  of  A  being 
all  bound  at  n ;  the 
pendulum  at  b  shows 
some  free  electricity, 

although  the  greater  part  of  the  electricity  of  B  is  bound  at  m.  Re- 
move A  and  B  from  each  other  and  the  bound  electricity  of  each  is 
set  free  and  both  a  and  b  fly  out  as  the  discs  are  separated.  The 
pith  balls  thus  seem  to  indicate  that  the  discs  are  more  highly  elec- 
trified when  they  are  thus  separated,  but  no  additional  charge  has 
been  given  to  either  A  or  B.  The  fact  is  that  while  B  was  near  A, 
the  capacity  of  B  was  largely  increased.  On  moving  it  away  from  A, 
its  capacity  was  diminished  and  the  same  quantity  of  electricity  elec- 
trified it  to  a  higher  potential  than  before.  The  presence  of  an  earth 
connected  plate  near  an  insulated  conductor  largely  increases  the  elec- 
tric capacity  of  the  latter,  enabling  it  to  condense  electricity  upon  the 
surface  nearest  the  opposing  plate,  at  which  surface  the  electrical  den- 
sity becomes  very  great. 

(b.)  If  A  and  B  are  pushed  up  close  to  C,  the  decrease  of  distance 
will  work  an  increase  of  the  inductive  action  and  a  still  larger  quan- 
tity may  be  accumulated  in  the  plates.  Thus,  the  capacity  of  a  con- 
denser depends,  in  part,  upon  the  nearness  of  the  plates  to  each  other. 


352.  Dielectrics  and  Specific  Inductive 
Capacity. — Substances  that  permit  inductive  electric 
influences  to  act  across  or  through  them  as  just  described 
are  called  dielectrics.  All  dielectrics  are  insulators,  but 


FRICTIONAL   ELECTRICITY. 


227 


equally  good  insulators  are  not  always  equally  good  dielec- 
trics. Glass  is  a  better  dielectric  than  ebonite  and  ebonite 
is  better  than  air.  The  capacity  of  a  condenser  is  greater 
when  the  dielectric  is  glass  than  it  is  when  the  dielectric 
is  air.  The  ratio  of  the  capacity  in  the  former  case 
to  the  capacity  in  the  latter  case  is  called  the 
specific  inductive  capacity  (or  specific  inductivity) 
of  glass.  Air  (at  0°  C.  and  760  mm. )  is  taken  as  the 
standard,  its  specific  inductive  capacity  being  unity. 

(a.)  The  old  idea  that  electric  induction  is  "  action  at  a  distance" 
is  wholly  disproved*  by  the  fact  that  different  substances  have  dif- 
ferent specific  inductive  capacities,  for  it  is  evident  that  the  dielec- 
tric itself  is  concerned  in  the  process.  Otherwise,  all  media  would 
allow  induction  to  take  place  across  them  with  equal  facility. 

(6.)  The  specific  inductivity  (sometimes  called  dielectric  capacity) 
assigned  to  various  substances  by  different  observers  varies  widely. 
Gordon  gives  the  following  results : 


Air 1.00      I  Ebonite 2.284 

Paraffin  (solid).l. 9936     Gutta  percha.  .2.462 

India  rubber.. 2.22       I  Sulphur 2.58 

Schiller  gives  the  specific  inductivity  of  white  mirror  glass  as  5.88 
to  6.34. 


Shellac 2.74 

Glass,  from 3.013 

"       to 3.258 


353.  The  Leydeii  Jar.— The  most  com- 
mon and,  for  many  purposes,  the  most  con- 
venient form  of  condenser  is  the  Leyden  jar. 
This  consists  of  a  glass  jar,  coated  within  and 
without  for  about  two-thirds  its  height  with 
tin-foil,  and  a  metallic  rod,  communicating 
by  means  of  a  small  chain  with  the  inner  coat 
and  terminating  above  in  a  knob.  The  upper 
part  of  the  jar  and  the  cork  which  closes  the 
mouth  of  the  jar  and  supports  the  rod  are  generally  coated 
with  sealing-wax  or  shellac  varnish  to  lessen  the  deposition 


FIG.  148. 


228  FRICTION  A  L   ELECTRICITY. 

of  moisture  from  the  air.  The  inner  coat  represents  the 
collecting  plate,  B\  the  glass  jar,  the  insulating  plate,  (7; 
the  outer  coat,  the  condensing  plate,  A,  of  Fig.  146. 

(a.)  Select  a  candy  or  fruit  jar  of  greenish  glass ;  paste  tin-foil 
within  and  without,  as  above  described,  using  flour  paste  ;  thrust  a 
wire  through  a  dry  cork  ;  bend  the  wire  so  that,  when  the  cork  is  in 
its  place,  the  wire  shall  touch  the  tin-foil  on  the  inside  of  the  bottle 
without  tearing  it ;  solder  the  upper  end  of  the  wire  to  a  smooth 
button  or  thrust  it  into  a  lead  bullet ;  charge  your  Leyden  jar  with 
a  few  sparks  from  the  electrophorus  and  take  a  shock. 

354.  Charging  the  Leydeii  Jar. — To  charge 
the  jar,  hold  it  in  the  hand,  as  shown  in  Fig.  149,  and  bring 
the  knob  near  the  prime  conductor  of  an  electrical  machine 
that  is  in  action  or  into  contact  with  it. 

(a.)  The  +  charge  thus  developed  on  the  inner  coat  acts  in- 
ductively through  the  glass,  repelling  the  +  electricity  which  escapes 
through  the  hand  to  the  earth  and  binding  its  —  electricity  to  the 
surface  in  contact  with  the  glass.  This  "  bound  "  negative  elec- 
tricity of  the  outer  coat,  in  turn,  binds  the  positive  of  the  inner  coat, 
which  then  may  receive  a  further  charge  and  so  on.  The  inner 
coat  will  receive  a  much  greater  quantity  of  electricity  than  it  pos- 
sibly could  were  it  not  for  the  attraction  of  its  opposite  on  the  outer 
coat.  If,  instead  of  holding  the  outer  coat  in  the  hand,  the  jar  be 
supported  upon  a  pane  of  glass  so  that  the  repelled  electricity  of  the 
outer  coat  cannot  escape,  the  jar  cannot  be  very  intensely  charged. 


FIG. 


(&.)  Thus  we  see  again  that  the  capacity  of  a  conductor  is  greatly 
increased  when  it  is  placed  near  a  conductor  charged  with  the  oppo- 


FRICTIONAL  ELECTRICITY. 

site  kind  of  electricity.  Its  capacity  being  increased,  it  can  receive  a 
greater  quantity  of  electricity  without  any  increase  of  potential.  Of 
course,  the  potential  of  the  charged  jar  cannot  exceed  that  of  the 
prime  conductor  or  other  charging  body. 

355.  Discharging  the  Leyden  Jar.— If  the  jar 

be  of  good  glass,  dry  and  free  from  dust,  it  will  retain  its 
charge  for  hours.  But  if  a  path  be  provided  by  which  the 
opposite  and  mutually  attracting  electricities  can  flow 
together,  they  will  do  so  and 
the  jar  will  be  instantaneously 
and  almost  completely  dis- 
charged. The  jar  might  be 
discharged  by  touching  the 
knob  with  the  finger,  the  sep- 
arated electricities  coming  to- 
gether through  the  person  of 

the  experimenter  and  the  earth.  In  this  case,  the  experi- 
menter will  feel  a  "shock."  If  the  charge  be  intense,  the 
shock  will  be  painful  or  even  dangerous.  It  is  better  to 
use  a  "  discharger,"  two  forms  of  which  are  represented  in 
Fig.  150.  This  consists  of  two  metal  arms  hinged  to- 
gether, bearing  knobs  at  their  free  ends  and  carried  by 
insulating  handles.  The  outer  coat  of  the  jar  should  be 
touched  first.  Why  ? 

(a.)  A  good  discharger  may  be  made  by  passing  a  piece  of  stout, 
copper  wire,  about  a  foot  long,  through  apiece  of  rubber  tubing  and 
providing  a  metal  knob  for  each  end  of  the  wire.  The  flexibility  of 
the  wire  avoids  the  necessity  for  a  hinged  joint. 

356.  The  Residual  Charge.— If  a  Leyden  jar  be 
charged,  discharged  and  left  for  a  little  time  to  itself,  it 
will  be  found  that  a  small,  second  spark  can  be  obtained. 


230 


FRICTIONAL  ELECTRICITY. 


TJiere  is  a  residual  charge  which  seems  to  have 
soaked  into  the  glass.  The  return  of  the  residual  charge 
is  hastened  by  tapping  the  jar.  The 
amount  of  the  residual  charge  varies 
with  the  time  that  the  jar  has  been 
left  charged ;  it  also  depends  on  the 
kind  of  glass  of  which  the  jar  is 
made.  (See  Appendix  J.) 

357.  The  Leyden  Jar  with 
Movable  Coats.— This  piece  of  appara- 
tus is  represented  by  Fig.  151.  The  upper 
part  of  the  glass  jar,  B,  is  coated  with  shel- 
lac varnish.  The  three  parts  being  placed 
together  in  proper  order,  B  within  A  and  G 
within  B,  the  jar  is  charged  in  the  usual  man- 
ner. The  inner  coat,  (7,  is  then  removed 
with  a  glass  rod  and  touched  with  the  hand 
to  discharge  it  fully.  B  is  then  lifted  out 
from  A  and  the  outer  coat  fully  discharged. 
The  three  parts  are  then  put  together  again 
and  found  to  be  able  to  give  nearly  as  strong 
a  spark  as  at  first.  This  seems  to  indicate 
upon  the  surfaces  of  the  glass  rather  than  upon 
the  surfaces  of  the  coats.  If,  when  the  charged  jar  is  in  pieces,  the 
thumb  be  placed  on  the  outer  surface  of  the  glass  and  the  forefinger 
of  the  same  hand  on  the  inner  surface,  a  very  slight  shock  is  per- 
ceptible. The  oppositely  charged  glass  molecules  that  come  into 
actual  contact  with  thumb  and  finger  respectively  are  discharged. 
By  changing  the  position  of  the  thumb  and  finger,  successive  little 
shocks  may  be  felt  as  successive  portions  of  the  inner  and  outer  sur- 
faces of  the  glass  are  discharged.  The  inner  coat  furnishes  a  means 
for  the  simultaneous  discharge  of  the  inner  layer  of  glass  molecules ; 
the  outer  coat  does  the  same  for  the  outer  layer  of  glass  molecules. 
Thus  all  or  nearly  all  of  the  electrified  glass  molecules  may  be  dis- 
charged simultaneously  instead  of  successively. 


FIG.  151. 


that  the  charge 


358.  The  Leyden  Battery,— The  effect  that  may 
be  produced  with  a  Leyden  jar  or  other  condenser  depends 


FRICTIONAL   ELECTRICITY. 


231 


upon  the  size  of  the  coats,  the  thinness  and  the  inductive 
capacity  of  the  glass.  But  a  large  jar  is  expensive  and 
requires  great  care ;  thin  glass  is  liable  to  perforation  by 


the  condensed  and  strongly  attracting  electricities  of  its 
two  coats.  To  obviate  both  of  these  d  ifficulties,  a  collection 
of  jars  is  used.  When  their  outer  coats  are  in  electric 
communication,  which  may  be  secured  by  placing  them 
in  a  tray  the  bottom  of  which  is  covered  with  tin-foil,  and 
their  inner  coats  are  connected  by  wires  or  metal  strips 
passing  from  rod  to  rod,  or  from  knob  to  knob,  the  ap- 
paratus is  called  a  Leyden  or  electric  battery.  "Tough- 
ened glass"  is  less  easily  pierced  than  ordinary  glass. 
Hence,  Leyden  jars  made  of  it  may  be  made  thinner  and, 
consequently,  Avill  hold  a  greater  charge  than  otherwise. 
The  battery  is  charged  and  discharged  in  the  same  way  as 
a  single  jar.  Great  care  is  needed,  for  if  the  discharge 


232  FRICTIONAL   ELECTRICITY. 

were  to  take  place  through  the  human  body  the  result 
would  be  serious  and  possibly  fatal.  The  "universal 
discharger,"  as  employed  with  the  Leyden  battery,  is 
shown  at  A  G  in  Fig.  152.  (See  Exp.  50.) 

(a.)  The  horizontal  rods  of  the  universal  discharger  may  be  sup- 
ported by  passing  them  through  corks  in  the  mouths  of  two  bottles. 
When  a  table  is  wanted  for  the  support  of  bodies  to  be  operated 
upon  by  the  discharge,  it  may  be  made  by  placing  a  small  plate  of 
glass  upon  the  open  mouth  of  a  bottle  of  the  same  height  as  those 
that  carry  the  rods  and  placing  the  third  bottle  between  the  other 
two. 

359.  The  Farad.— The  farad  is  the  capacity  of  a 
condenser  that  will  be  raised  to  a  potential  of  one  volt  by 
a  charge  of  one  coulomb  of  electricity  (§§  382,  387).  Such 
a  condenser  would  be  too  large  to  be  constructed.  The 
micro-farad  (=0.000001  farad)  is,  therefore,  chosen  as 
the  practical  unit  of  electrical  capacity.  The  ca- 
pacity of  three  miles  of  an  Atlantic  cable  is  about  one 
micro-farad.  A  micro-farad  condenser  contains  about 
3,600  square  inches  of  tin-foil.  A  farad  equals  10~9  of  an 
electro-magnetic  unit  of  capacity  (§  451).  See  App.  M  (5). 

(a.)  A  coulomb  in  a  farad  gives  a  volt. 
Coulombs 


Farads  = 


Volts 


36O.    Submarine    Cable    Condensers.  —  An 

ocean  cable  forms  a  condenser,  the  water  forming  the 
outer  coating ;  the  conducting  wire,  the  inner  coating ; 
while  the  insulating  layers  of  gutta-percha  correspond 
to  the  glass  of  the  Leyden  jar.  When,  for  example,  one 
end  of  a  submerged  cable  is  connected  to  the  -f  pole  of 
a  powerful  battery,  +  electricity  flows  into  it.  Before 
any  signal  can  be  received  at  the  other  end,  enough  elec- 


FRICTIONAL  ELECTRICITY.  233 

tricity  must  flow  in  to  charge  the  cable  to  a  considerable 
potential,  an  operation  which  may,  in  the  case  of  long 
cables,  require  some  seconds.  It  is  a  serious  obstacle  to 
signalling  with  speed  through  the  Atlantic  cables. 

(a.)  Imagine  a  mile  of  insulated  cable  wire  to  be  coiled  up  in  a  tub 
of  water  (Fig.  153),  one  end,  JV".  being  insulated.  The  other  end  is 
joined  up  through  a  long 
coil  galvanometer,  G,  to 
the  +  pole  of  a  large  bat- 
tery., whose  —  pole  is 
joined  by  a  wire  to  the 
water  in  the  tub.  As 
soon  as  this  is  done,  the 
needle  of  the  galvanom-  JTIG  jg^. 

eter  will  show  a  violent 

deflection,  +  electricity  rushing  through  it  into  the  interior  of  the 
cable  and  a  —  charge  being  accumulated  on  the  outside  of  it  where 
the  water  touches  the  gutta-percha.  The  flow  will  go  on,  though 
diminishing,  until  the  cab.le  is  fully  charged,  taking,  perhaps,  an 
hour.  Now  remove  the  battery  and  close  the  circuit.  The  charge 
in  the  cable  will  rush  out  through  the  galvanometer,  which  will 
show  an  opposite  deflection.  The  charge  will  continue  "to  soak 
out "  for  a  long  time. 

361.  Modes  of  Discharge. — An  electrified  con- 
ductor may  be  discharged  in  at  least  three  ways,  viz.,  by 
the  disi*uptive>  discharge,  by  the  convective  discharge 
and  by  the  conductive  discharge.  The  discharge  in  any 
of  these  ways  is  accompanied  by  a  transformation  of  .en- 
ergy. Sound,  light,  heat,  chemical  action  and  other  phe- 
nomena are  produced. 

Experiment  35. — Present  a  knuckle  of  the  hand  or  a  metal  knob 
fco  the  prime  conductor  of  an  electric  machine  and  "draw  sparks" 
therefrom.  (See  Fig.  169.)  For  short  distances,  the  spark  is  straight. 
If  the  distance  be  made  somewhat  greater,  the  spark  takes  a  sinuous 
and  forked  form  as  though  floating  dust  particles  served  as  stepping- 
stones  and  rendered  a  crooked  path  the  easiest.  If  the  charge  be 


234 


FRICTION AL  ELECTRICITY. 


very  powerful,  the  spark  will  take  the  zigzag  form  so  familiar  in  the 

lightning-stroke.  When  the  machine  is  vigorously  worked  in  the 
dark,  the  apparently  continuous  discharge  into 
the  air  produces  a  luminous  appearance  at  the 
ends  of  the  conductor.  This  appearance,  known 
as  a  brush,  may  be  improved  by  holding  a  large, 
smooth,  metal  globe  at  a  distance  a  little  too  great 
for  the  passage  of  a  spark.  When  the  discharge 
takes  place  from  the  rounded  end  of  a  wire  ex- 
tending from  the  conductor,  a  quiet,  phosphor- 

escent glow,  as  shown  in  Fig.  154,  will  often  appear  at  and  near  the 

end  of  the  wira 


FIG.  154. 


362.  The  Disruptive  Discharge. — A  discharge 
of  electricity  taking  place  suddenly  through  a  non-con- 
ductor is  called  a  disruptive  discharge,  e.g.,  the  spark  and 
brush  drawn  from  an  electric  machine  in  action.  The 
glow  is  either  a  continuous  discharge  or  one  of  exceed- 
ingly small  period.  Perhaps,  it  is  a  high  order  of  con- 
vective  discharge. 

Experiment  36. — Attach  a  pointed  wire  to  the  prime  conductor 
of  the  electric  machine.     The  flame  of  a  candle  held  near  will  be 
blown  away,  as  shown  in 
Fig.  155.     If  the  candle  be 
placed    upon    the     prime 
conductor  and    a    pointed 
conductor  be  held  in  the 
hand  near  the  candle,  the 
flame  will  still  be  blown 
away. 


363.  The  Con- 
vective  Dis- 
charge. —  When  elec- 
tricity of  high  poten- 
tial  accumulates  with 

so  great  a  density  as  to  electrify  the  neighboring  particles 
of  air  which,  driven  by  electric  repulsion,  fly  off  carrying 


FlG 


FRICTIONAL  ELECTRICITY.  235 

part  of  the  charge  with  them,  we  have  what  is  called  the 
convective  discharge.  Such  discharges  are  best  mani- 
fested in  gases  at  low  pressure,  in  tubes  exhausted  by  an 
air-pump.  (Exp.  70.) 

364.  The  Conductive  Discharge.— The  flow 
of  a  continuous  current  of  electricity  constitutes  the  con- 
ductive discharge.     When  electricity  flows  through  a  wire 
from  the  prime  conductor  of  an  electric  machine  to  the 
rubbers  or  from  the  positive  pole  of  a  voltaic  cell  or  bat- 
tery to  the  negative,  we  have  a  conductive  discharge.     It 
will   be  considered  in  the  section  especially  devoted  to 
voltaic  electricity. 

365.  Atmospheric  Electricity. — The  phenom- 
ena of  atmospheric  electricity  are  of  three  kinds  : 

1.  A  continual  slight  electrification  of  the  air,  best  ob- 

served in  fair  weather. 

2.  The  familiar  phenomena  of  thunder  storms. 

3.  The  Aurora  Borealis. 

366.  The  First  Kind.— During  fair  weather,  the 
air  above  the  surface  of  the  earth  is  usually  electrified  posi- 
tively, a  negative  electrification  being  extremely  rare.     In 
stormy  weather,  it  is  more  often  —  than  -f  and  frequently 
changes  from  one  kind  to  the  other  several  times  in  an 
hour.     The  higher  up  we  go  to  observe  the  usual  +  elec- 
tricity of  the  air,  the  higher  its  potential  is  found  to  be. 
The  evaporation  of  water  by  the  sun's  heat  and  the  fric= 
tion  of  moving  masses  of  air  probably  contribute  to  the 
presence  of  atmospheric  electricity. 

367.  Thunder    Storms. — We  have  already  seen 
(g  341)  that  a  solid  conductor  can  not  be  charged  through- 


236  FRICTION AL  ELECTRICITY. 

out  its  substance,  the  charge  residing  upon  the  surface. 
The  same  is  true  of  liquids,  but  aeriform  bodies  may  be 
charged  bodily,  the  individual  molecules  being  so  much 
more  widely  separated.  Dry  air  being  a  poor  conductor, 
the  air  particles  discharge  their  electricity  into  each 
other  slowly  and  with  difficulty.  The  electricity  thus 
prevented  from  accumulating  has  a  low  potential  and, 
hence,  gives  few  manifestations  of  its  presence.  The 
minute  particles  of  water  floating  in  the  air  being  better 
conductors  than  the  air  itself  become  more  highly  charged. 
As  they  fall  and  unite,  the  potential  of  their  charges  in- 
creases. 

(a.)  "Suppose  eight  small  drops  to  join  into  one.  That  one  will 
have  eight  times  the  quantity  of  electricity  distributed  over  the  sur- 
face of  a  single  sphere  of  twice  the  radius  and,  therefore,  of  twice 
the  capacity  (for  the  electrical  capacities  of  spheres  are  proportional 
to  their  radii)  of  the  original  drops."  The  capacity  being  thus  in- 
creased only  two  fold  while  the  quantity  is  increased  eight  fold,  the 
potential  becomes  four  times  as  great.  Thus  the  potential  of  a 
cloud  may  rise  by  the  union  of  electrified  drops. 

•  368.  Lightning1, — When  an  electrified  cloud  floats 
over  the  earth,  separated  from  it  by  a  layer  of  insulating 
air,  the  inductive  influence  of  the  cloud  renders  the  ground 
beneath  oppositely  electrified.  Then  the  cloud,  ground 
and  insulating  air  correspond  respectively  to  the  inner 
and  outer  coatings  and  the  insulating  glass  of  a  Leyden 
jar.  As  the  charge  of  a  Leyden  jar  may  be  made  so  in- 
tense  that  the  mutual  attraction  of  the  separated  elec- 
tricities will  result  in  their  rushing  together  and  thus 
piercing  the  jar  (|  358),  so  the  charge  of  a  cloud  may  be- 
come sufficiently  intense  to  overcome  the  resistance  of  the 
air  and  a  lightning  stroke  ensues.  Two  clouds  charged 


FRICTIONAL  ELECTRICITY.  237 

with  opposite  electricities  may  float  near  each  other. 
Then  they,  with  the  intervening  air,  may  be  looked  upon 
as  constituting  a  huge  Leyden  jar.  Thus,  we  may  see 
the  lightning  leaping  from  cloud  to  earth,  or  from  clond 
to  cloud.  Such  electric  sparks  are  sometimes  more  than 
a  mile  in  length,  showing  a  difference  of  potential  greater 
than  that  of  3,000,000  Daniell's  cells.  The  duration  of 
the  spark  or  flash  is  not  more  than  0.00001  of  a  second. 
The  danger  from  any  lightning  stroke  has  passed  when  we 
hear  the  crash.  The  identity  of  lightning  with  electricity, 
though  long  suspected,  was  first  proved  by  Franklin's 
famous  kite  experiment.  (See  Exp.  64.) 

Experiment  37. — Bring  the  point  of  a  knife-blade  near  the  con 
ductor  of  an  electric  machine  in  operation  and  notice  the  instant  cessa- 
tion of  sparks.  The  quiet  passage  of  electricity  from  the  earth 
neutralizes  the  charge  of  the  conductor  and  restores  the  electric 
equilibrium.  In  the  same  way,  a  lightning-rod  tends  to  restore  the 
electric  equilibrium  of  the  cloud  and  prevent  the  dangerous  dis- 
charge. 

369.  Lightiiing-Rods. — The  value  of  lightning- 
rods  depends  upon  the  tendency  of  electricity  to  follow 
the  best  conductor  and  upon  the  effect  of  pointed  con- 
ductors upon  electrical  density  (§  342).  The  lightning- 
rod  should,  therefore,  be  made  of  a  good  conductor ; 
copper  is  better  than  iron.  It  should  terminate  above  in 
one  or  more  points,  tipped  with  some  substance  that  may 
be  corroded  or  fused  only  with  extreme  difficulty.  Plati- 
num and  iridium  are  metals  that  satisfy  these  conditions 
very  well.  The  rod  should  extend  above  the  highest  point 
of  the  building  in  order  to  offer  the  electricity  the  easiest 
path  to  the  ground.  It  is  important  to  have  each  pro- 
jecting part  of  the  building,  as  chimneys,  towers  and 


238  FRICTIONAL  ELECTRICITY. 

gables,  protected  by  a  separate  rod.  All  metal  work  about 
the  roof  or  chimneys  should  be  connected  with  the  rod. 
The  rod  should  afford  an  unbroken  connection ;  the  joints, 
if  there  be  any,  should  be  carefully  made.  The  rod 
should  terminate  below  in  water,  or  in  earth  that  is  always 
moist.  It  is  well  to  connect  it  with  underground  water- 
pipes  when  possible  or  with  a  large  metal  plate.  Personal 
attention  should  be  given  to  this  matter  when  the  rod  is 
put  up  as,  being  under  ground  and  out  of  sight,  this  part 
of  the  rod  is  not  easily  inspected  subsequently.  A  rod 
having  a  Hunted  tip,  a  broken  joint  or  terminating 
in  dry  earth  is  more  dangerous  than  no  rod  at  all. 
Lightning-rod  insulators  are  undesirable. 

(a.)  The  greatest  value  of  a  lightning-rod  is  due  to  its  quiet  work 
in  the  prevention  of  the  lightning  stroke.  For  this  quiet  but  very 
valuable  service,  few  persons  ever  give  the  rod  any  credit.  Every 
leaf  of  the  forest  and  every  blade  of  grass  is  a  pointed  conductor 
acting  in  the  same  way. 

(6.)  There  is  some  question  as  to  the  space  protected  by  a  rod,  but 
the  following  is  a  good  rule :  The  protected  space  is  a  cone  having 
its  apex  at  the  tip  of  the  rod  and  having  a  base  the  radius  of  which 
is  equal  to  the  height  of  the  cone. 

37O.  The  Aurora  Borealis. — The  aurora  borealis 
or  "northern  light"  is  frequently  seen  in  northern  re- 
gions; beyond  the  Arctic  circle  it  is  of  almost  nightly 
occurrence.  Sometimes  its  streamers  of  light  radiate  like 
the  ribs  of  a  fan  or  form  an  arch  across  the  northern  sky, 
as  shown  in  Fig.  156.  But,  as  seen  in  this  country,  it 
more  often  appears  as  a  few  streamers  of  a  pale  tint. 
Similar  lights  are  seen  in  south  polar  regions  and  are 
called  aurora  australis. 

The  atmosphere,  in  its  upper  strata,  is  highly  rarefied 
and  conducts  electricity  as  do  the  rarefied  gases  in  Geissler 


FRICTIONAL   ELECTRICITY. 


tubes  (Exp.  70).     There  is  little  doubt  that  the  aurora  ig 
due  to  electric  discharges  in  this  rarefied  air.    The  appear- 


FIG.  156. 

ance  of  an  aurora  is  generally  accompanied  by  a  "  mag- 
netic storm"  or  irregular  disturbance  that  affects  all  of 
the  compass  needles  over  a  considerable  part  of  the  earth. 

371.  Apparatus    and    Experiments.  —  It    is 

neither  necessary  nor  very  desirable  that  all  of  the  follow- 
ing experiments  be  performed.  Several  of  them  involve 
the  same  principle ;  but  one  teacher  may  have  one  piece  of 
apparatus  and  another,  another  piece.  Additional  experi- 
ments may  be  found  in  "  The  First  Principles  of  Natural 
Philosophy,"  pp.  174-176. 

Experiment  38. — Place  a  tin  plate  containing  a  handful  of  small 
bits  of  tissue  paper  upon  the  prime  conductor  of  an  electric  machine. 
Work  the  machine  and  thus  produce  an  imitation  snow  storm. 


240 


FRl  CTIONAL   ELECTRICITY. 


Experiment  39. — The  "  metallic  plates  and  dancing  images  "  are 
represented  in  Fig.  157.  The  images  are  made  of  pith.  The  upper 
plate  is  in  communication  with  the  prime  conductor , 
the  lower  one,  with  the  earth.  When  the  machine 
is  worked,  the  images  dance  in  a  very  ludicrous 
manner.  Explain.  Pith  balls  may  be  substituted 
for  the  images,  the  resulting  phenomena  being  known 
as  "  Volta's  hail."  The  experiment  may  be  simplified 
by  electrifying  the  inner  surface  of  a  glass  tumbler 
by  rubbing  it  upon  the  knob  of  the  prime  conductor 
and  placing  the  tumbler  over  some  pith  balls  on  the 
table. 

Experiment  40. — Place  a  dozen  pith  balls  or  some 
FIG.   157.        bits  of  tissue  paper  on  a  table  between  two  books 
about  2  inches  (5  cm.)  thick.     Place  a  pane  of  glass 
upon  the  books  as  shown  in  Fig.  158. 
Rub  the  upper  surface  of  the  glass 
with  the  silk  pad  mentioned  in  §  302 
(or  a  silk  handkerchief)  and   notice 
the  lively  dance  of  the  pith  balls.  FIG.  158. 

Experiment  41. — In  the  "electric  chime,"  represented  in  Fig. 
159,  the  outer  bells  are  to  be  put  into  communication  with  the  prime 
conductor;  the  central  bell  is  in  communication  with  the  earth. 


FIG.   159. 


FIG.   160. 


The   clappers  are  suspended  by  silk  threads.     Work  the  machine 
slowly  ;  the  bells  will  begin  to  ring.     Explain. 


miCTIONAL  ELtiCTtttClTY.  241 


Experiment  42.— In  the  "Leyden  jar  and  bells,"  shown  in  Fig. 
180,  the  left-hand  bell  is  in  communication  with  the  outer  coat  of  the 
jar;  the  clapper  is  suspended  by  a  silk  thread.  When  the  jar  is 
charged  and  placed  in  position  as  represented,  the  bells  begin  to 
ring  and  continue  to  do  so  for  a  considerable  time.  Explain. 

Experiment  43. — In  the  "  electric  swing,"  shown  in  Fig.  161, 
the  boy  is  suspended  by  silk  cords.  One  of  the 
insulated  knobs  is  in  communication  with  the 
earth;  the  other  with  the  prime  conductor. 
When  the  machine  is  worked,  the  boy  swings  to 
and  fro.  Explain. 


Experiment  44.—  If  a  pupil  hold  a  Leyden 
jar  by  the  outer  coat  and,  by  a  wire,  connect  the 
knob  of  the  jar  with  the  prime  conductor,  his  pIG 

knuckle  will  attract  the  balanced  lath  (Exp.  5) 
when  the  machine  is  worked.    Explain. 

Experiment  45.  —  Fasten  a  small  paper  kite  by  a  linen  thread  to 
the  prime  conductor.  When  the  machine  is  worked,  the  kite  wilV 
float  around  the  knob.  Explain. 

Experiment  46.  —  Fasten  one  end  of  a  long,  small,  copper  wire  to 
the  prime  conductor.  Near  the  other  end  of  the  wire,  tie  a  silk  cord 
and  hang  it  from  the  ceiling  or  other  support  so  that  the  end  of  the 
vertical  part  of  the  wire  shall  be  at  a  convenient  height.  To  this 
end  of  the  wire  attach  a  tassel  about  four  or  five  inches  long  made 
of  many  strips  of  light  tissue  paper.  Work  the  machine  and  the 
leaves  will  diverge.  Explain.  Extend  toward  it  your  clenched  fist  ; 
the  leaves  seek  the  fist.  Explain.  Instead  of  your  fist,  hold  a  needle 
toward  the  tassel  ;  it  will  be  blown  away.  Explain.  Hold  the 
needle  upright  under  the  tassel.  The  strips  will  collapse.  Explain. 

Experiment  47.  —  Stand  upon  the  insulating  stool  and  place  your 
left  hand  upon  the  prime  conductor  of  the  electric  machine.  Hold  in 
your  right  hand  a  sewing-needle  with  the  tip  of  the  forefinger  cover- 
ing the  end  of  the  needle.  Bring  the  right  hand  cautiously  near  the 
gold-leaf  electroscope.  Notice  the  divergence  of  the  leaves.  Now 
uncover  the  point  of  the  needle  and  bring  it  near  the  electroscope. 
Notice  the  marked  and  immediate  increase  in  the  divergence  of  the 
leaves.  Explain. 

Experiment  48.—  Place  an  "electric  whirl"  (which  consists  of 
a  set  of  horizontal  wire  arms  radiating  from  a  pivot-supported  centre, 


242 


FRICTIONAL  ELECTRICITY. 


the  pointed  ends  being  all  bent  in  the  same  direction)  upon  the  prime 
conductor.  Work  the  machine  and  the  arms  will  revolve.  (Fig. 
162.)  Explain. 


Experiment  49.  —  The  "electric  or- 
rery," represented  in  Fig.  163,  is  a  pret- 
ty modification  of  the  "  electric  whirl." 
The  short,  balanced  bar  is  provided  with 
a  pointed  conductor  to  produce  rotary 
motion  upon  its  supporting  pivot,  which 
is  one  end  of  the  long  balanced  bar. 
This  longer  bar 
is  also  provided 
with  a  pointed 
conductor  and 
supported  i  n 
turn  upon  a 
pivot,  which 


FIG.  162. 


may  be  attached  FIG.  163. 

to     the     prime 

conductor.     When  the  machine  is  worked,  the  long  bar  revolves 
upon  its  fixed  pivot ;  the  short  bar  revolves  upon  its  moving  pivot. 

Experiment  50. — Half  fill  a  wide,  glass  vessel  with  water.  Within 
this,  place  a  glass  beaker  and  fill  it  to  the  same  level  with  water. 
By  a  wire,  connect  the  water  in  the  outer  vessel  with  the  earth ;  in 
similar  manner,  connect  the  water  in  the  beaker  with  the  electric 
machine.  Give  the  handle  of  the  machine  a  single  turn.  Dipping 
one  finger  into  the  outer  water  and  another  into  the  inner  water,  a 
shock  is  felt.  Explain. 

Experiment  51.— Let  a  pupil  stand  upon  an  insulating  stool  (a 
board  supported  by  four  warm  tumblers  will  answer)  and  place  his 
left  hand  upon  the  prime  conductor.  Let  him,  with  his  right  hand, 
clasp  the  left  hand  of  another  pupil  not  insulated,  their  hands  being 
prevented  from  actual  contact  by  an  intervening  sheet  of  india-rub- 
ber cloth.  After  the  machine  has  been  worked  a  moment,  let  the 
insulated  pupil  remove  his  left  hand  from  the  prime  conductor  and 
clasp  the  free  hand  of  his  companion.  At  this  moment  of  clasping 
hands,  a  shock  will  be  felt  Explain. 

Experiment  52.— Cover  one  knob  of  the  discharger  with  gun  cot- 
ton  sprinkled  with  powdered  rosin.  When  the  Ley  den  jar  is  dis- 
charged with  this  discharger,  the  cotton  and  rosin  are  ignited 


FRICTIO NA L  ELECTRICITY. 


243 


Bring  the  covered  knob  of  the  discharger  into  contact  with  the  knob 
of  the  jar  with  a  quick  motion. 

Experiment  53. — The  "  electric  bomb,"  represented  in  Fig.  104, 
may  be  made  of  ivory,  heavy  glass,  or  thorough- 
ly seasoned  wood.  The  ends  of  the  two  metal 
wires  are  rounded  and  placed  a  short  distance 
apart.  The  bomb  may  be  filled  with  gun- 
powder. One  wire  is  connected  by  a  chain 
with  the  outer  coat  of  a  charged  Leyden  jar. 
The  other  wire  is  to  be  connected  with  the 
inner  coat  by  a  wet  string  and  the  discharger. 
The  spark  between  the  ends  of  the  two  wires 
ignites  the  powder.  Then  try  the  experiment 
with  air  instead  of  powder.  FIG.  164. 

Experiment   54. — Fig,  165  illustrates  a  method  of  igniting  an 

inflammable  liquid,  like 
ether  or  alcohol,  by  the 
electric  spark.  Through 
the  bottom  of  a  small 
glass  vessel,  a,  passes  a 
metal  rod,  having  a  knob 
at  its  upper  extremity. 
The  lower  end  of  this 
rod  may  be  brought  into 
electrical  connection  with 
the  outer  coat  of  a  Ley- 
den  jar.  Enough  ether 
or  alcohol  is  poured  into 
a  just  to  cover  the  knob. 
When  the  jar  is  dis- 
charged in  the  way 
shown  in  the  figure,  the 
spark  ignites  the  liquid. 
If  alcohol  is  used,  it  may 
have  to  be  warmed  to 
render  the  experiment 
successful. 

Experiment  55. — Let 
FIG.  165.  a  pupil,  standing  on  an 

insulating  stool,  become 
charged  by  holding  one  hand  on  the  prime  conductor  when  the 


244  FRICTION AL   ELECTRICITY. 

machine  is  in  operation.  If  he  then  bring  his  knuckle  to  a  metal 
burner  from  which  a  jet  of  gas  is  issuing,  a  spark  will  pass  be- 
tween  the  knuckle  and  the  burner,  igniting  the  gas.  An  Argand 
or  Bunsen  burner  answers  well  for  this  experiment.  The  experi- 
ment may  be  modified  by  using,  instead  of  the  knuckle,  an  icicle 
held  in  the  hand.  The  gas  burner  may  be  replaced  by  a  pupil  (not 
insulated)  holding  a  spoonful  of  ether  or  of  chloroform  which  readily 
gives  off  an  easily  combustible  vapor. 

Experiment  56. — The  "universal  discharger,"  shown  in  Fig.  166, 
consists  of  a  glass  table  and  two  insulated  metal  rods.  (See  §  358  a.) 

Balls,  points  and  pincers  are 
provided  for  use  at  the  adja- 
cent ends  of  the  rods  which  are 
supported  upon  sliding  and 
hinged  joints,  so  that  they  may 
be  easily  placed  in  any  desir- 
able position.  Cover  the  ad- 
jacent ends  of  the  two  rods 
FIG.  166.  with  metal  balls  and  place  them 

upon  the  glass  table,  a  small 

distance  apart.  Connect  the  balls  by  a  very  fine  wire.  One  of  the 
rods  is  to  be  connected  by  a  wire  or  chain  with  the  outer  coats  of  a 
powerful  battery  ;  the  other  rod  is  to  be  connected,  by  the  discharger, 
(Fig.  150)  with  the  inner  coats  of  the  battery.  The  current  thus 
passed  along  the  fine  wire  may  heat  it  to  incandescence,  melt  or 
even  vaporize  it. 

Experiment  57.— Prick  a  profile  portrait  of  Franklin  or  some  other 
design  in  a  sheet  of  thin  card  board.  Paste  two  pieces  of  tin-foil  to 
the  ends  of  the  card  and  join  them  with  a  piece  of  gold  leaf  placed 
over  the  pricked  design.  Place  a  piece  of  white  paper  or  silk  on  the 
other  side  of  the  card  and  have  the  whole  tightly  screwed  up  be- 
tween two  boards,  leaving  the  edges  of  the  tin-foil  strips  accessible. 
Discharge  a  Leyden  battery  through  the  gold  leaf,  thus  volatizing 
it,  sending  the  disintegrated  particles  through  the  holes  in  the  card 
board  and  obtaining  an  impression  of  the  portrait. 

Experiment  58. — Fig.  167  represents  "Volta's  pistol,"  which 
consists  of  a  metal  vessel  through  one  side  of  which  passes  an  in- 
sulated metal  rod  with  knobs  at  both  ends.  The  knob  at  the  inner 
end  of  this  rod  is  near  the  opposite  wall,  so  that  a  spark  may  easily 
be  made  to  pass  between  the  knob  and  the  body  of  the  pistol.  The 
pistol  being  filled  with  a  mixture  of  illuminating  gas  and  common 


24G 


FRICTIONAL   ELECTRICITY. 


sulated  support,  lower  a  second  pointed  conductor  until  it  touches 
the  pane  at  the  oil.  Through  these  two  pointed  conductors  (Fijr. 
168),  discharge  a  Leyden  jar  or  battery.  Unless  the  glass  is  very  thin, 
.a  single  jar  will  not  be  sufficient.  If  the  experiment  fails  the  first 
time,  do  not  use  the  same  piece  of  glass  for  the  second  trial.  A  plate 
of  glass,  6  cm.  thick,  has  been  pierced  by  means  of  a  powerful  in 
duction  coil. 

Experiment  61. — With  corks,  plug  the  ends  of  a  glass  tube  filled 
with  water.  Through  the  corks,  introduce  copper  wires  until  the 
ends  in  the  water  are  within  a  quarter  of  an  inch  of  each  other. 
Through  these  wires,  discharge  a  Leyden  jar.  The  mechanical  shock 
due  to  the  repulsion  of  the  electrified  water  molecules  will  often 
break  the  tube. 

Experiment  62.— Charge  a  Leyden  jar.  In  discharging  it,  hold 
a  stiff  card  between  the  knob  of  the  jar  and  the  knob  of  the  di» 


FIG.  169. 

charger.     A  hole  will  be  pierced  through  the  card.     By  the  side  of 
tW§  Uole  in  the  card,  make  another  with  a  pin.     Any  one  can  tell 


FRICTIONAL  ELECTRICITY. 


247 


by  examination  of  the  pin-hole  from  which  side  of  the  card  it  waa 
pierced ;  it  is  burred  on  only  one  side.  Not  so  with  the  perforation 
made  by  this  discharge ;  it  is  burred  on  both  sides. 

Experiment  63. — One  of  the  inevitable  experiments  with  an  elec- 
tric machine  consists  in  "  drawing  sparks "  from  the  conductor  by 
the  hand  (Fig.  169).  When  the  potential  of  the  separated  electrici 
ties  becomes  sufficient  to  overcome  the  resistance  of  the  intervening 
air,  they  recombine  with  a  sharp,  explosive  sound  and  brilliant  flasi: 
t)f  light.  (§362.) 

Experiment  64.— Divide  a  circle 
into  black  and  white  sectors,  as  shown 
in  Fig.  170,  and  attach  it  to  a  whirl- 
ing table  ($  74).  Revolve  it  so  rapidly 
that  the  colors  blend  and  the  disc  ap- 
pears a  uniform  gray.  Darken  the 
room  and  illuminate  the  rapidly  re- 
volving disc  by  the  electric  spark 
from  a  Ley  den  jar.  The  disc  will 
appear  at  rest  and  each  sector  will 
appear  separate  from  its  neighbors. 
This  shows  that  the  duration  of  the 
electric  spark  is  less  than  the  persist- 
ence of  vision. 


FIG.  170. 


Experiment  65. — In  a  dark  room,  place  a  piece 
of  loaf  sugar  in  contact  with  the  outside  coat  of  a 
charged  Leyden  jar.  Place  one  knob  of  the  dis- 
charger upon  the  sugar  and  bring  the  other  near 
the  knob  of  the  jar.  When  the  jar  is  discharged 
thus  through  the  sugar,  the  sugar  will  glow  for 
some  time. 

Experiment  66. — The  "luminous  jar,"  repre 
sented  in  Fig.  171,  is  a  modified  Leyden  jar.  The 
outer  coat  consists  chiefly  of  a  layer  of  varnish 
sprinkled  over  with  metallic  powder.  A  strip  of 
tin-foil  at  the  bottom  affords  means  of  communica- 
tion with  the  earth.  A  similar  band  at  the  upper 
edge  of  the  outer  coat  is  provided  with  an  arm,  as 
shown  in  the  figure.  The  rod  of  the  jar  is  curved 

so  as  to  bring  the  knob  near  the  projecting  arm  of  the  outer  coat. 

The  jar  is  suspended  by  the  curved  rod  from  the  prime  conductor 


248 


FRICTIONAL    ELECTRICITY. 


FIG.  172. 


FIG.  173. 


and  its  lower  strip  of  tin-foil  connected 
with  the  earth.  When  the  machine  is 
worked,  sparks  pass  between  the  knob 
and  the  projecting  arm.  In  a  dark  room, 
the  metallic  powder  coat  will  be  beauti- 
fully illuminated  at  the  passage  of  each 
such  spark. 

Experiment    67. — The      "  luminous 
pane"  is  represented   in  Fig.   172.      A. 
continuous  tin-foil  strip  is  pasted  back 
and  forth  upon  the  surface  of  a  plate  of 
glass.    The  upper  end  of  this  strip  is  con- 
nected with  the  prime  conductor ;    the 
lower  end  with  the  earth.     A   series  of 
breaks  in  this  continuous  conductor  may 
be  made  by  cutting  it  across  with  a  sharp 
pen-knife.    When  the  machine  is  worked, 
a  small  spark  will  appear  at  each  break 
thus  made.      These  breaks  may  be  ar- 
ranged so  as  to  represent  a  flower,  star, 
arch,  word  or  other  de- 
sign.    The  sparks  are 
really    successive,   but 
they  seem  to  be  simul- 
taneous. 


Experiment     68.— 

The  "luminous  globe  " 
is  represented  in  Fig. 
173  and  the  "  luminous 
tube  "in  Fig.  174.  The 
first  of  these  consists 
of  a  hollow  glass  globe, 
on  the  inner  surface  of 
which  small  discs  of 
tin-foil  are  placed  very 
near  each  other.  The 
first  disc  is  in  connec- 
tion with  the  prime 
conductor,  and  the  last 
one  with  the  ground. 
When  the  machine  is 


FIG.  174. 


miCTIONAL   ELECTRICITY. 


249 


worked,  bright  sparks  appear  at  each  break  between  the  discs.  The 
construction  and  action  of  the  luminous  tube  are  similar.  All  of 
these  luminous  effects  are  best  exhibited  in  the  dark. 

Experiment  69. — If  two  barometer 
tubes,  united  at  the  top,  be  filled  with 
mercury  and  inverted  over  two  cups  of 
mercury,  as  shown  in  Fig.  175,  a  Torri- 
cellian vacuum  will  be  formed  at  the 
bend.  When  the  mercury  of  one  cup  is 
connected  with  the  prime  conductor  and 
that  of  the  other  with  the  earth,  the  up- 
per part  of  fhe  tube  (containing  only  mer- 
curic and  other  vapors)  is  filled  with  light. 
The  luminosity  may  be  increased  by 
raising  the  temperature  and  thus  in- 
creasing the  density  of  the  aeriform  con- 
ductor. (A  true  vacuum  will  not  con- 
duct electricity.)  The  apparatus  may 
be  put  into  the  circuit  of  an  induction 
coil  instead  of  connecting  it  with  the 
prime  conductor  and  the  earth. 

Experiment  70.— "Geissler's  Tubes" 
are  sealed  glass  tubes  containing  a 
highly  rarefied  vapor  or  gas.  Platinum 
wires  are  sealed  into  the  glass  at  each 
end,  to  conduct  the  electric  current  to 
the  interior  of  the  tube.  The  brilliancy  FlG>  I75> 

and  beauty  of  the  light,  the  great  variety 

of  effects,  color  and  fluorescence,  are  indescribable.  They  are  made 
in  great  variety  of  form  and  size  and  filled  with  rarefied  vapors  and 
gases  of  many  kinds.  A  few  of  the  forms  are  represented  in.  Fig. 


FIG.  176. 

176.    They  may  be  used  in  the  dark  with  an  electric  machine  or  an 
induction  coil  (§  459). 


250 


FRICTIONAL  ELECTRICITY. 


Experiment  71.— In  "Crookes's  Tubes,"  devised  in  many  forms 
by  Prof.  Crookes  for  his  investigations  of  the  phenomena  of  "  radiant 
matter"  (§  59  6),  the  tension  of  the  contained  gas  is  reduced  to  about 
one  millionth  of  an  atmosphere,  far  below  that  of  Geissler's  tubes, 
Under  the  influence  of  the  electric  discharge,  matter  seems  to  be 
radiated  from  the  negative  pole  in  straight  lines  and  in  directions 
perpendicular  to  the  radiating  surface. 


FIG.  177. 

(a.)  One  of  these  tubes,  used  to  show  that  radiant  matter  "  may 
exert  mechanical  action,  is  shown  in  Fig.  177.  It  consists  of  a  highly 
f-xhausted  glass  tube  containing  a  glass  railway.  The  axle  of  a 
small  wheel  revolves  on  the  rails,  the  spokes  of  the  wheels  carrying 


FIG.  178. 

mica  paddles.     Pole  pieces  are  fused  in  through  the  glass,  as  repre- 
sented.    Whichever  pole  is  made  negative,  "  radiant  matter  "  darts 


FRICTIONAL   ELECTRICITY.  251 

from  it  along  the  tube,  strikes  the  upper  paddles,  causing  the  wheel 
to  roll  along  the  railway.  By  reversing  the  poles,  the  motion  of  the 
wheel  may  be  stopped  and  reversed. 

(6.)  To  show  that  "radiant  matter"  may*  be  deflected  from  a 
straight  line,  he  devised  the  tube  shown  in  Fig.  178.  The  negative 
pole,  a  &,  is  in  the  form  of  a  shallow  cup.  A  mica  screen,  c,  shields 
the  mica  paddle-wheel,  ef.  By  holding  one  pole  of  the  magnet,  g, 
over  the  tube,  the  matter  radiated  from  a  b  is  deflected  upward  and 
the  wheel  caused  to  revolve  like  an  overshot  water-wheel.  By  hold- 
ing the  other  pole  of  the  magnet  over  the  tube,  the  molecular  stream 
is  deflected  downward  and  the  wheel  caused  to  revolve  as  an  under- 
shot water-wheel.  (See  Appendix  C.) 

312.  Relation  of  Electricity  to  Energy-— 

The  work  necessarily  performed  in  operating  an  electric 
machine  is  not  all  expended  in  overcoming  inertia  and 
friction.  Much  of  it  is  employed  in  producing  electric 
separation.  It  matters  not  whether  this  separation  be 
the  separation  of  two  fluids  or  of  something  else.  What- 
ever be  the  nature  of  the  realities  separated,  me- 
chanical, kinetic  energy  is  employed  in  the  separa- 
tion and  converted  into  the  potential  variety  (§  159). 
An  electrified  pith  hall  or  a  charged  Leyden  jar  is  simply 
an  electro  statical  reservoir  of  potential  energy.  In  the 
discharging  of  such  a  body,  the  passage  of  the  current  is 
accompanied  by  a  loss  of  potential  energy.  What  becomes 
of  this  energy  ?  This  leads  us  to  look  for  effects  due  to 
it,  to  work  done  by  it.  Many  illustrations  of  work- thus 
done  have  been  furnished  in  the  experiments  just  de- 
scribed. In  every  case  of  electric  attraction  or  repulsion, 
we  have  an  evident  reconversion  of  this  potential  energy 
into  mechanical  kinetic  energy.  We  shall  soon  see  that 
the  sound,  heat  and  light  accompanying  electric  dis- 
charges are  forms  of  energy  due  to  the  conversion  of  the 
potential  energy  of  electric  separation.  We  shall  see  other 


252  FRICTION AL  ELECTRICITY. 

effects,  more  or  less  powerful,  when  we  come  to  study 
voltaic  and  other  forms  of  current  electricity. 

EXERCISES. 

1.  (a.)  If  a  gold-leaf  electroscope  be  placed  within  a  tin  pail  which 
is  insulated  and  electrified,  what  will  be  the  action  of  the  electro- 
scope?    (&.)  Explain. 

2.  (a.)  Why  may  one  obtain  a  stronger  spark  from  a  Leyden  jar 
than  from  the  machine  by  which  it  is  charged?    (&.)  A  Leyden  jar 
standing  upon  a  glass  plate  cannot  be  strongly  charged.     Why  ? 

3.  (a.)  A  globe  that  is  polished  will  remain  electrified  longer  than 
one  that  is  not  polished.     Why?    (&.)  Can  you  devise  an  appendage 
to  the  outer  coat  of  a  Leyden  jar,  so  that  it  may  be  charged  when 
standing  upon  a  plate  of  glass  ? 

4.  (a.)  Describe  the  plate  electric  machine.     (&.)  Explain   its  ac- 
tion,   (c.)  Explain  the  action  of  the  electrophorus. 

5.  (a.)  A  minute  after  the  discharge  of  a  Leyden  jar,  a  second  and 
feebler  spark  may  generally  be  obtained.     Explain.     (&.)  State  two 
uses  of  lightning-rods. 

6.  (a.)  Having  a  metal  globe  positively  electrified,  how  could  you 
with  it  negatively  electrify  a  dozen  globes  of  equal  size  without 
affecting  the  charge  of  the  first  ?    (&.)  How  could  you  charge  posi- 
tively one  of  tne  dozen  without  affecting  the  charge  of  the  first? 

7.  Can  you  devise  a  plan  by  which  a  series  of  Leyden  jars,  placed 
upon  a  glass  plate,  may  be  simultaneously  charged,  the  first  posi- 
tively, the  second  negatively,  the  third  positively,  the  next  nega- 
tively and  so  on? 

8.  How  would  you  prove  that  there  is  no  electrification  within  a 
closed  conductor? 

9.  At  what  distance  from  a  small  sphere  charged  with  28  units  of 
electricity  must  you  place  a  second  sphere  charged  with  56  units 
that  one  may  repel  the  other  with  a  force  of  32  dynes  ?    Ans.  7  cm. 

10.  If  a  number  of  Leyden  jars  be  separately  charged  in  the  or- 
dinary way  and  then  connected  in  series,  so  that  the  outer  coating 
of  one  is  connected  with  the  inner  coating  of  the  next,  will  the  po- 
tential of  the  battery  be  changed  and  in  what  way  ? 

11.  Will  the  "  striking  distance"  of  a  battery  of  Leyden  jars  in 
series  be  less  or  greater  than  the  striking  distance  (i.e.,  the  greatest 
distance  at  which  the  discharge  by  spark  will  take  place  through 
air)  of  a  battery  of  the  same  number  of  similar  cells  arranged  abreast 
as  shown  in  Fig.  152  ? 


FRICTIONAL  ELECTRICITY.  253 

12.  In  what  way  may  an  electric  charge  be  divided  into  three 
equal  parts  ? 

13.  Suppose  two  similar  conductors  to  be  electrified,  one  with  a 
+   charge  of  5  units  and  the  other  with  a  —  charge  of  3  units. 
They  are  made  to  touch  each  other.     When   they  are  separated, 
what  will  be  the  charge  of  each  ? 

Ans.  One  unit  of  +  electricity. 

14.  "Why  are  telegraphic  signals  through  a  submerged  cable  re- 
tarded in  transmission  ? 


254  FRICTIONAL  ELECTRICITY. 

Recapitulation. — To  be  amplified  by  the  pupil  for 
review. 

KINDS  AND  NAMES. 
ELECTROSTATIC   LAWS. 
ELECTRICAL    UNITS   AND   TESTS. 
ELECTROSCOPES. 

s>rtMrMin-ris\iu  (  CONDUCTORS,  NON-ELECTRICS. 

CONDUCTION \  INSULATORS,  ELECTRICS. 

TENSION,  POTENTIAL  AND   CAPACITY. 

f  BY   CONTACT. 
ELECTRIFICATION.  |  [  POLARIZATION. 

ELECTROPHORUS. 


CJ 


BY  INDUCTION. 


ELECTRIC   MACHINES 


Q 

££}  L  SOURCE    OF    ENERGY, 

U 

PROVISIONAL  THEORY. 

Q   \ 

DISTRIBUTION    OF  j  ON  SURFACE. 
CHARGE.  1  DENSITY. 


CONDENSERS 


DIELECTRICS. 
INDUCTIVE  CAPACITY. 

LEYDEN  JAR. 
LEYDEN  BATTERY. 

SUBMARINE  CABLES. 


f  DISRUPTIVE. 

DISCHARGE  ........  I  CONVECTIVE. 

[  CONDUCTIVE. 

f  THUNDER  STORMS.  J  LIGHTNING. 

ATMOSPHERIC    E.     J  '  LIGHTNING-RODS 

I  AURORA  BOREALIS. 

L  RELATION  TO  ENERGY. 


HI, 


VOLTAIC     AND    THERMO-ELECTRICITY. 

373.  Chemical  Action.  —  All  chemical  changes  are 
accompanied  by  electric  separation.     The  substances  acted 
upon  may  be  solid,  liquid  or  aeriform,  but  the  chemical 
action  between  liquids  and  metals  gives  results  the  most 
satisfactory.     Electricity  thus  developed  is  called  voltaic 
or  galvanic  electricity.    Its  energy  is  derived  from  the 
potential  energy  of  chemical  affinity  (§  7). 

374.  Current  Electricity.  —  The  principal  classes 
of  electric  currents  are  as  follows: 

(1.)    Currents  produced  by  chemical  action,  i.  e., 

voltaic  electricity. 
(2.)    Currents    produced    by    heat,    i.  e.,    thermo- 

electricity. 
(3.)    Cuwents  produced  by  other  electric  currents 

or  by  magnets,  i.  e.,  induced  electricity. 

(a.)  We  have  seen  that,  when  a  body  having  an  electrical  charge 
is  properly  connected  with  another  of  lower  potential,  there  is  a 
transfer  of  electricity  from  the  former  to  the  latter.  This  implies 
that  there  is  an  electric  current.  But  this  current  is  only  momentary 
and  of  little  importance  in  comparison  with  the  currents  that  we  are 
about  to  consider.  Current  electricity  may  differ  from  static  elec- 
tricity in  quantity,  electromotive  force,  etc.,  but  not  in  its  nature. 

375.  The  Voltaic    Current.  —  When  a  strip  of 
copper  and  one  of  zinc  are  placed  in  dilute  sulphuric  acid 

25 


256  VOLTAIC  ELECTRICITY. 

or  in  a  battery  solution  like  the  one  already  used,  the  two 
strips  being  connected  above  the  acid  by  a  wire  conductor, 

a  current  of  electricity  is  produced. 

The  apparatus   here  described 

is  called  a  voltaic  or  galvanic 

element  or  cell. 

(a)  For  voltaic  purposes,  the  sulphuric 
acid  should  be  diluted  by  slowly  pouring 
the  acid  into  ten  or  twelve  times  its  bulk 
of  soft  water.  Do  not  pour  the  water 
into  the  acid. 

FIG  179  376    Wnence  the  Energy 

of  Current  ? — The  energy  of  the  current  is  due  to  the 
potential  energy  of  chemical  affinity  existing  between  the 
acid  and  the  zinc.  As  the  chemical  affinity  between  coal 
and  oxygen  develops,  in  the  furnace,  a  form  of  kinetic  en- 
ergy that  we  call  heat,  so  the  potential  energy  of  chemical 
separation  between  the  acid  and  the  zinc  develops,  in  the 
cell,  the  two  varieties  of  kinetic  energy,  heat  and  electric 
current.  The  coal  is  consumed  in  the  one  case ;  the  zinc, 
in  the  other. 

377.  Direction  of  the  Current. — For  this  pro- 
duction of  the  electric  current,  it  is  necessary  that  the 
liquid  have  a  greater  action  upon  one  plate  than  upon  the 
other.  The  plate  that  is  more  vigorously  acted  upon  by 
the  liquid  constitutes  the  generating  or  positive  plate ;  the 
other,  the  collecting  or  negative  plate.  This  relation  of 
the  plates  determines  the  direction  of  the  current.  In 
the  liquid,  the  current  is  from  the  positive  to  the 
negative  plate;  in  the  wire,  the  current  is  from 
the  positive  to  the  negative  electrode.  In  each 


VOLTAIC  ELECTRICITY.  257 

case,  the  current  passes  from  -f  to  — .     The  direction 
of  the  current  is  indicated  by  arrows  in  Fig.  179. 

When  the  wires  from  the  two  plates  are  in  contact,  it 
is  said  that  the  circuit  is  closed ;  when  the  plates  are  not 
thus  in  electric  connection,  it  is  said  that  the  circuit  is 
broken. 

378.  Electrodes. — It  may  help  the  memory  to  sup- 
pose that,  in  a  voltaic  cell,  two  currents,  opposite  in  kind 
and  direction,  are  simultaneously  produced.     It  will  be 
readily  understood,  by  keeping  in  mind  the  direction  of 
these  two  currents,  that,  if  the  circuit  be  broken,  negative 
electricity  will  accumulate  at  the  end  of  the  wire  attached 
to  the  positive  plate  and  positive  electricity  at  the  end  of 
the  wire  attached  to  the  negative  plate.     Tliese  ends  of 
the  wires  are  then  called  poles  or  electrodes.      The 
negative  pole  is  attached  to  the  positive  plate  and 
vice  versa.     The  plate  or  electrode  from  which  the 
current  flows  is  -f  ;  that  toward  which  the  current 
flows  is  — .      Strips  of  platinum  are  often  fastened  to  the 
ends  of  the  wires;  these  platinum  strips  then  constitute 
the  electrodes. 

379.  Resistance. — Every  electric  circuit  offers  a  re- 
sistance  to  the  passage  of  the  current.      This  resistance 
will,  of  course,  depend  largely  upon  the  materials  used  for 
the  circuit.     (See  Appendix  K.) 

( 1.)  With  a  conducting  wire  of  a  given  material, 
the  resistance  is  proportional  to  the  length.  If  the 
resistance  of  a  mile  of  telegraph  wire  be  13  ohms,  the  re- 
sistance of  50  miles  of  such  wire  will  be  (13  ohms  x  50  =) 
650  ohms. 

( 2. )   With  a  conducting  wire  of  a  given  material, 


258  VOLTAIC  ELECTRICITY. 

the  resistance  is  inversely  proportional  to  its  sec* 
tional  area,  to  the  square  of  its  diameter  or  to  its 
weight  per  linear  unit.  If  one  conductor  be  twice  the 
diameter  of  another  made  of  the  same  length  and  material, 
the  sectional  area  or  the  weight  per  foot  or  yard  will  be 
(22=)  four  times  as  great  and  the  resistance  of  the  first 
will  be  one-fourth  as  great  as  that  of  the  second.  If  they 
be  made  of  the  same  material  and  length,  one  weighing 
twice  as  much  per  foot  as  the  latter,  the  resistance  of  the 
former  will  be  half  as  great  as  that  of  the  latter.  (See 
Appendix  I.) 

(3.)  The  resistance  of  a  conducting  wire  of  given 
length  and  thickness  depends  upon  the  material 
of  which  it  is  made,  i.  e.,  upon  the  specific  resist- 
ance of  the  material.  (See  Appendix  K,  [2].) 

(4.)  The  resistance  of  a  given  conductor  may  vary  with 
its  temperature.  (See  Appendix  K,  [3].) 

(a.}  Conductivity  and  resistance  are  reciprocals,  but  it  is  more 
common  to  speak  of  the  resistances  of  conductors  than  of  their  con- 
ductivities. 

38O.   The  Practical  Unit  of  Resistance.—. 

The  practical  unit  of  resistance  is  called  an  ohm. 
A.  m>egohm  is  a  million  ohms.  A.  microhm  is  one- 
millionth  of  an  ohm.  The  ohm  is  the  resistance  of  a 
column  of  mercury  one  square  millimeter  in  section  and  at 
the  freezing  temperature  (0°  0.).  The  exact  length  of  this 
column  is  to  be  determined  experimentally  by  an  interna- 
tional commission.  A  recent  determination  of  the  value 
of  the  ohm  (probably  the  best  yet  made)  gives  the  mercury 
column  a  length  of  106.3  cm.  If  the  pupil  will  get,  from 
some  dealer  ia  electrical  supplies,  40  ft.  of  No.  24  insulated 


VOLTAIC  ELECTRICITY.  259 

copper  wire  (see  Appendix  I),  he  will  have  a  very  good 
standard  ohm. 

(a.)  A  galvanized  iron  (telegraph)  wire,  4  millimeters  in  diameter 
and  100  meters  long,  or  a  pure  copper  wire,  1  millimeter  in  diameter 
and  48  meters  long,  has  a  resistance  of  about  one  ohm.  An  ohm 
equals  109  absolute  electro-magnetic  units  (§  452).  (For  the  measure- 
ment of  resistances,  see  Appendix  M,  [2  and  3].) 

381.  Examples.— (a.)  If  the  resistance  of  130  yd.  of  copper 
wire,  y1^  inch  in  diameter,  be  one  ohm,  what  is  the  resistance  of  260 
yd.  of  copper  wire,  -fa  inch  in  diameter  ?     Since  the  diameter  of  the 
first  wire  is  twice  that  of  the  second,  the  sectional  area  of  the  first  will 
be  four  times  that  of  the  second.     (Areas  of  circles  are  proportional 
to  the  squares  of  their  diameters.)     Therefore,  the  resistance  of  the 
same  length  (130  yds.)  of  the  smaller  wire  will  be  four  times  that  of 
the  larger  wire,  or  4  ohms.     But  the  second  or  smaller  wire  is  twice 
as  long.     Therefore,  its  resistance  will  be  twice  (ff$)  as  great,  or  8 
ohms.  Ans.  8  ohms. 

(b.)  What  is  the  resistance  of  20  yd.  of  platinum  wire,  0.016  inch 
in  diameter,  if  the  resistance  of  200  yd.  of  copper  wire,  134  mils  in 
diameter,  is  0.34  ohm  and  the  relative  resistances  of  platinum  and 
copper  are  as  11.8  :  1  ?  (A  mil  is  the  one -thousandth  of  an  inch. 
The  term  is  frequently  used  in  descriptions  of  wire.) 

on        /1Q4\  2      1 1  Q 

0.34  ohm  x  ~  x  I  ^ )    x  ^  =  26.95  ohms. 
200      \  16  / 

Ans.  26.95  ohms. 

382.  Electromotive  Force. — Electromotive  force 
(often  written  E.  M.  F.  or  simply  E.)   is  the  mysterious 
power  that  causes  a  transfer  of  electricity  from  one  point 
to  another.     It  is  somewhat  analogous  to  hydrostatic  pres- 
sure.    Wherever  there  is  difference  of  potential,  there  is 
E.  M.  F.     The  terms  are  not  synonymous,  although,  for 
convenience,  E.  M.  F.  is  often  expressed  as  difference  of 
potential   and    vice   versa.     The    E.   M.  F.  of   a  voltaic 
cell  depends  upon  the  nature  of  the  materials  used  and 
not  upon  the  size  of  the  plates  or  the  distance  between 
them, 


260  VOLTAIC  ELECTRICITY. 

Tl%e  unit  of  electromotive  force  is  called,  a  volt. 
A  microvolt  is  one-millionth  of  a  volt. 

A  volt  is  a  little  less  than  the  E.  M.  F.  of  a  Daniell  cell 
(§  394),  which  measures  1.079  volts. 

(a.)  A  volt  equals  108  absolute  electro-magnetic  units  (§  452). 
(For  the  measurement  of  E.  M.  F.  see  Appendix  M,  [4].) 

383.  Internal   Resistance.  —  We  may  imagine 
that  the  two  plates  of  a  voltaic  cell  are  connected  by  a 
liquid  prism.     The  greater  the  distance  between  the  plates, 
the  longer  this  prism  and  the  greater  its  resistance.     The 
larger  the  plates,  the  larger  the  prism  and  the  less  its  re- 
sistance.    (See  Appendix  M,  [3].) 

When  the  circuit  is  closed,  hydrogen  is  set  free  by  the 
decomposition  of  the  liquid  and  rises  from  the  surface  of 
the  negative  plate.  Gases  are  poor  conductors.  Hence, 
the  hydrogen  bubbles  that  often  adhere  to  the  negative 
plate  increase  the  internal  resistance  of  the  cell  by  lessen- 
ing the  effective  surface  of  the  plate  (§  389).  This  ten- 
dency of  the  hydrogen  to  adhere  to  the  plate  is  one  of 
the  practical  difficulties  to  be  overcome  in  working  a 
voltaic  cell  or  battery. 

384.  Fall  of  Potential.— The  existence  of  a  cur- 

rent is  evidence  of  a 
difference  of  potential 
at  any  two  consecu- 
tive points  of  the  cir- 
cuit. It  may  he  well 
to  compare  the  flow 
of  electricity  with  the 
flow  of  water  in  hori- 
zontal pipes  and  difference  of  potential  with  difference  of 


VOLTAIC  ELECTRICITY.  2G1 

hydrostatic  pressure.  Let  Fig.  180  represent  a  vessel  filled 
with  water.  The  tap  at  0  is  closed  and  the  water  stands  at 
the  same  level  in  all  of  the  vertical  tubes  (§  234)  showing 
that  there  is  no  difference  of  pressure  and,  consequently,  no 
liquid  flow.  Similarly, 
when  there  is  no  differ- 
ence of  potential  there  is 
no  electric  flow.  But 
when  the  tap  at  C  is 
opened,  as  represented 

in  Fig.  181,  it  is  noticed 

',>:i      ,  .     .,  FIG.  181 

that  the  level  in  the  ver- 
tical tubes  becomes  lower  as  we  pass  from  A  toward  C.  The 
height  of  water  in  each  vertical  tube  indicates  the  pressure 
at  that  part  of  the  tube,  B.  This  difference  in  hydrostatic 
pressure  produces  a  flow  of  water.  In  much  the  same  way, 
if  the  electric  potential  of  a  voltaic  circuit  be  measured  at 
different  points,  it  will  be  found  to  decrease  from  the  +  pole 
to  the  —  pole.  If  the  circuit  be  a  wire  of  uniform  size 
and  material,  the  resistance  offered  by  it  will  be  uniform 
and  the  potential  will  fall  uniformly.  If,  however,  the  cir- 
cuit be  made  to  have  a  varying  resistance  in  different  parts, 
the  potential  will  fall  most  rapidly  along  the  parts  of 
greatest  resistance.  For  the  whole  or  any  part  of  the 
circuit,  the  fall  of  potential  will  be  proportional  to  the 
resistance. 

(a.)  A  number  of  hydraulic  motors  may  be  worked  "  hi  series " 
upon  a  given  water  pipe,  the  outflow  of  the  first  being  the  supply  of 
the  second.  The  work  done  in  any  motor  may  be  determined  from 
the  quantity  of  water  flowing  through  the  pipe  or  motor  per  second 
and  tJie  difference  between  the  supply  pressure  and  the  back  pressure 
at  the  motor.  There  will  be  a  fall  of  pressure  between  the  two  sides 
of  the  motor  at  work.  The  more  work  the  motor  has  to  do,  the  more 


262  VOLTAIC    ELECTRICITY. 

resistance  it  will  offer  to  the  flow  of  water  and  the  greater  the  fall  of 
pressure.  Similarly,  a  number  of  telegraphic  instruments  or  electric 
lamps  may  be  placed  in  series  upon  an  electric  circuit.  The  work 
done  in  each  instrument  or  lamp  will  depend  upon  the  current 
strength  and  the  difference  of  potential  between  the  two  terminals 
of  the  instrument  or  lamp.  There  will  be  a  fall  of  a  certain  number 
of  volts  between  the  two  terminals,  depending  upon  the  intervening 
resistance. 

385.  The  Ampere. — The  strength  of  current  or  its 
rate  of  flow  (often  called  its  intensity)  will  depend  upon 
electromotive  force  and  resistance,   increasing  with  the 
former  and  decreasing  with   the   latter.     The  unit    of 
current   is   called   an  ampere.     One-thousandth  of 
an  ampere  is  called  a  milli-ainpere.     At  any  given 
instant,  the  current  is  the  same  at  every  part  of  the  circuit. 

(a.)  The  telegraphic  currents  commonly  used  on  main  lines  vary 
from  5  to  15  milli-amperes.  The  currents  commonly  used  in  electric 
arc  lamps  vary  from  7  to  20  amperes. 

(&.)  The  strength  of  a  current  may  be  measured  by  its  heating 
<-Tect  (§471)  or  by  the  products  of  electrolysis,  as  in  the  case  of  the 
wacer  voltameter  (§  410).  But  currents  are  generally  measured  by  in- 
s  ruments  like  the  galvanometer  (§418),  or  by  their  electro-magnetic 
effects.  An  instrument  so  used  is  called  an  ammeter  (abbreviated 
from  ampere-meter).  An  ampere  equals  0.1  or  10"1  of  an  absolute 
electro-magnetic  unit  (§  452). 

386.  Ohm's    Law. — The    strength    of   current 
varies   directly   as  the   E.  M.  F.   and  inversely  as 
the  resistance.     This  resistance  is  the  total  resistance  of 
the  circuit,  including  the  internal  resistance  of  the  cells 
or  dynamo  and  the  resistance  of  the  external  circuit. 

Volts  E  E 

-  =  Amperes,  or  Q—  -5-    .-.   E=  C  x  R ;  R  —  -7,- 
(trims  H 

Standards  for  strength  of  current  have  not  yet  been 
made. 


VOLTAIC   ELECTRICITY.  263 

(a.)  Ohm's  great  service  (A.D.,  1827)  to  electrical  science  consisted 
largely  in  the  introduction  of  the  accurate  ideas,  electromotive 
force,  current  strength  and  resistance.  "Before  his  time,  the 
quantitative  circumstances  of  the  electric  current  had  been  indicated 
in  a  very  vague  way  by  the  use  of  the  terms  '  intensity '  and 
'  quantity/  to  which  no  accurately  defined  meaning  was  attached." 

(6.)  If  we  have  a  difference  of  potential  that  secures  an  E.  M.  F. 
of  18  volts,  and  if  the  total  resistance  of  the  circuit  be  3  ohms,  the 
strength  of  the  current  will  be  6  amperes,  18  -f-  3  =  6.  The 
analogy  of  flowing  water  will  again  help  us.  The  rate  at  which  the 
water  is  delivered  will  depend  upon,  not  only  the  head  or  pressure 
(corresponding  to  E.  M.  F.),  but  also  upon  the  resistance  it  meets  with 
in  flowing,  If  the  pipe  be  small  and  crooked  or  if  it  be  choked  with 
sand  or  sawdust,  the  water  will  flow  in  a  small  stream  even  though 
the  pressure  be  great. 

Experiment  72. — Make  four  coils  or  spools  of  insulated  wire  as 
follows :  (See  Appendix  I.) 

No.  1,  of  100  feet  of  No.  16  gauge,  copper. 

No.  2,  of  100        "      "    30      " 

No.  3,  of   50        "      "    30      " 

No.  4,  of    50       "      "    30      "       german  silver. 

Place  the  wire  of  the  first  spool  and  a  galvanometer  (§  418)  in  the 
circuit  of  one  cell  and  note  the  number  of  degrees  of  deflection  of 
the  galvanometer  needle.  Put  the  second  spool  in  place  of  the  first. 
The  smaller  deflection  shows  that  (other  things  being  equal)  the 
No.  16  wire  transmits  more  current  than  the  No.  30.  Why  ?  Then 
add  the  third  spool  to  the  circuit.  The  still  smaller  deflection  shows 
that  (other  things  being  equal)  a  long  wire  transmits  less  current 
than  a  shorter  one.  Why  ?  Remove  the  second  spool  from  the 
circuit  and  note  the  deflection  of  the  galvanometer.  Put  the  fourth 
spool  in  place  of  the  third.  The  diminished  deflection  shows  that 
(other  things  being  equal)  a  german  silver  wire  transmits  less  current 
than  a  copper  wire.  Why  ?  With  any  one  of  the  spools  in  the  cir- 
cuit, compare  the  galvanometer  deflections  produced  by  a  Bunsen 
cell  and  by  a  gravity  cell  and  notice  that  the  former  gives  the 
stronger  current. 

Note. — These  experimens  give  very  crude  results  but,  such  as 
they  are,  they  fairly  represent  the  measurements  that  prevailed 
until  recently.  More  accurate  measurements  with  numerical  repre- 
sentations of  the  results  are  now  demanded.  The  rapid  advances  of 


264  VOLTAIC  ELECTRICITY. 

electrical  science  within  the  last  few  decades  have  been  very  largely 
due  to  the  adoption  of  definite  units  and  accurate  determinations. 
(See  Appendix  M.) 

387.  The  Coulomb.— The  unit  of  quantity  is 
called  the  coulomb.  It  is  the  quantity  of  elec- 
tricity given  by  a  one  ampere  current  in  one 
second.  A  ten  ampere  current  will  give  thirty  coulombs 
in  three  seconds. 

(a.)  The  word  "  quantity "  was  formerly  used  in  the  sense  in 
which  the  word  "intensity"  was  used  in  §  385,  while  the  latter 
word  was  used  as  if  it  depended  upon  E.  M.  F.  alone.  But  quantity 
of  electricity,  clearly,  depends  upon  the  strength  of  the  current  and 
the  time  that  the  current  flows.  A  coulomb  equals  0.1  or  10"1  of  an 
absolute  electro-magnetic  unit  of  quantity  (§  452). 

EXEKCISES. 

1.  What  length  of  No.  10  pure  copper  wire  (B.  &  S.)  will  have  a 
resistance  of  1  ohm  ?    (See  Appendix  I.)  Ans.  961.54  ft. 

2.  A  given  battery  has  an  E.  M.  F.  of  12  volts.     The  internal 
resistance  is  8  ohms.      The  resistance  of  the  external  circuit  is  4 
ohms.     What  is  the  strength  of  the  current  ? 

3.  The  4  cells  of  a  given  battery  are  connected  so  that  the  total 
E.  M.  F.  is  4  volts  and  the  internal  resistance  is  20  ohms.     The 
external  circuit  has  a  resistance  of  20  ohms.    What  is  the  strength 
of  the  current  ?  Ans.  0.1  ampere. 

4.  What  length  of  copper  wire  4  mm.  in  diameter  will  have  the 
same  resistance  as  12  yd.  of  copper  wire  1  mm.  in  diameter  ? 

Ans.  192yd. 

5.  The  4  cells  of  a  given  battery  are  connected  so  as  to  give  an 
E.  M.  F.  of  2  volts  and  to  have  a  total  internal  resistance  of  10  ohms. 
The  external  circuit  is  a  stout  copper  wire  with  a  resistance  so  small 
that  it  may  be  ignored.     What  is  the  current  strength  ? 

6.  The  same  battery  is  used  with  a  telegraphic  sounder  in  the 
circuit.     This  instrument  has  a  resistance  of  5  ohms.     What  is  the 
current  strength  ?  Ans.  133  milli-amperes. 

7.  The  resistance  of  47  ft.  of  copper  wire,  22  mils  in  diameter, 
being  1  ohm,  find  the  resistance  of  200  yd.  of  copper  wire  134  mils 
in  diameter.  Ans.  0.34  ohm. 

If  you  do  not  know  what  a  mil  is,  consult  the  Index. 


VOLTAIC  ELECTRICITY.  265 

$.  A  battery  has  a  current  of  2  amperes  flowing  through  a  total 
resistance  of  9  ohms.     What  is  the  E.  M.  F.  ? 

9.  The  E.  M.  F.  of  a  battery  is  10  volts.     The  current  is  1  ampere. 
The  external  resistance  is  5  ohms.     What  is  the  internal  resistance 
of  the  battery  ?  Ans.  5  ohms. 

10.  The  potential  of  a  current  falls  45  volts  between  the  two 
terminals  of  an  incandescence  lamp.     The  current  measures  1.25 
amperes.     What  is  the  resistance  of  the  lamp  ?         Ans.  36  ohms. 

Jgp^  If  you  do  not  know  what  an  incandescence  lamp  is,  consult 
the  Index. 


266  VOLTAIC  ELECTRICITY. 

388.  Amalgamating  the  Zinc.— Ordinary  com- 
mercial zinc  is  far  from  being  pure.      The   chemically 
pure  metal  is  expensive.    When  impure  zinc  is  used,  small 
closed  circuits  are  formed  between  the  particles  of  foreign 
matter  and  the  particles  of  zinc.     This  local  action,  which 
takes  place  even  when  the  circuit  of  the  cell  or  battery  is 
broken,  rapidly  destroys  the  zinc  plate  and  contributes 
nothing  to  the  general  current.     This  waste,  which  would 
not  occur  if  pure  zinc  were  used,  is  prevented  by  fre- 
quently amalgamating  the  zinc.     This  is  done  by  clean- 
ing the  plate  in  dilute  acid  and  then  rubbing  it  with 
mercury. 

(a.)  The  method  of  amalgamating  battery  zincs  practised  by  the 
author  is  as  follows :  In  a  glass  vessel  placed  in  hot  water,  dissolve 
15  cu.  cm.  of  mercury  in  a  mixture  of  170  cu.  cm.  of  strong  nitric 
acid  and  625  cu.  cm.  of  hydrochloric  (muriatic)  acid.  When  the 
mercury  is  dissolved,  add  830  cu.  cm.  of  hydrochloric  acid.  When 
the  liquid  has  cooled,  immerse  the  battery  zinc  in  it  for  a  few 
minutes,  remove  and  rinse  thoroughly  with  water.  The  liquid  may 
be  used  over  and  over  until  the  mercury  is  exhausted.  The  quan- 
tity here  mentioned  will  suffice  for  200  ordinary  zincs  or  more. 
Keep  the  liquid,  when  not  in  use,  in  a  glass-stoppered  bottle. 

389.  Polarization. — It  was  stated  in  §  383  that  the 
accumulation  of  hydrogen  bubbles  at  the  negative  plate 
increases  the  internal  resistance  of  the  cell.      But  the 
hydrogen  affects  the  current  in  another  way.     It  acts  like 
a  positive  plate  (being  almost  as  oxidizable  as  the  zinc) 
and  sets  up  an  opposing  electromotive   force    that   tends 
to  set  a  current  in  the  opposite  direction.     A  cell  or  bat- 
tery in  this  condition  is  said  to  be  polarized.     Some- 
times, as  a  result  of  polarization,  the  strength  of  the  cur- 
rent falls  off  very  greatly  within  a  few  minutes  after  clos- 
ing the  circuit.     (See  §  414.) 


VOLTAIC  ELECTRICITY.  26? 

390.  Varieties  of  Voltaic  Cells.— All  voltaic 
belong  to  one  of  two  classes  : 

(1.)  Those  using  only  one  liquid. 
(2.)  Those  using  two  liquids. 

All  of  the  earlier  batteries  were  composed  of  one-liquid 
3ells. 

Note. — When  dilute  sulphuric  acid  is  mentioned  in  connection  with 
cells  and  batteries,  it  may  be  understood  that  one  volume  of  acid  to 
ten  or  twelve  volumes  of  water  is  meant. 

391.  Smee's  Cell.— A  Smee's  cell 
is  represented  by  Fig.  182.     It  consists  of 
a  platinized  silver  plate  placed  between 
two  zinc  plates  hung  in  dilute  sulphuric 
acid.    The  hydrogen  bubbles  accumulate 
at  the  points  of  the  rough  platinum  sur- 
face and  are  more  quickly  carried  up  to 
the  surface  of  the  liquid  and  thus  gotten 
rid  of.     The  cell  has  an  available  electro- 
motive force  of  about  0.47  volt.  FIG.  182. 

392.  Potassium  Di-chromate  Cell.— The  po- 
tassium di-chromate  cell  has  a  zinc  plate  hung  between 
two  carbon  plates.     A  solution  of  potassium  di-chromate 
(bi-chromate  of  potash)  in  dilute  sulphuric  acid  is   the 
liquid  used.     The  hydrogen  is  given  an  opportunity  for 
chemical  union  as  fast  as  it  is  liberated.     The  E.  M.  F.  of 
this  cell  is  great  to  start  with  (from  1.8  to  2.3  volts),  but 
it  falls  very  quickly  when  the  external  resistance  is  small. 
It  quickly  recovers  and  may   be  used  with  advantage 
where  powerful    currents  of    short    duration   are  often 
wanted.     It  is  the  only  single  liquid  cell  that  is  free  from 
polarization.     It  is  sometimes  called  the  Grenet  cell. 


268 


ELtiCTRtClTY. 


FIG.  183. 


(a.)  The  bottle  form  of  this  cell,  represented  in  Fig.  183,  is  the 
most,  convenient  for  the  laboratory  or  lecture  table.  By  means  of  the 
sliding  rod,  the  zinc  plate  may  be  raised  out 
of  the  solution  when  not  in  use.  Thus  ad- 
justed, the  cell  may  remain  for  months  with- 
out any  action,  if  desired,  and  be  ready  at  a 
moment's  notice. 

(6.)  One  of  the  best  proportions  for  the  solu- 
tion is  as  follows  :  One  gallon  of  water,  one 
pound  of  potassium  di-chromate  and  from  a 
half  pint  to  a  pint  of  sulphuric  acid,  according 
to  the  energy  of  action  desired.  A  small 
quantity  of  nitric  acid  added  to  the  solution 
increases  the  constancy  of  the  battery  by  oxi- 
dizing the  nascent  hydrogen  and  thus  forming 
water. 

(c.)  The  following  recipe  is  good :  Pour  167 
cu.  cm.  of  sulphuric  acid  into  500  cu.  cm.  of 
water  and  let  the  mixture  cool.  Dissolve  115 
g.  of  potassium  di-chromate  in  335  CM.  cm.  of 
boiling  water  and  pour,  while  hot,  into  the  dilute  acid.  When  cool, 
it  is  ready  for  use. 

393.  The  Leclaiiche  Cell.— This  cell,  shown  in 
Fig.  184,  contains  a  zinc  plate  or  rod  and  a  porous,  earthen- 
ware cup  containing  the  carbon  plate. 
The  space  between  the  carbon  plate 
and  the  cup  is  filled  with  fragments 
of  carbon  and  powdered  peroxide  of 
manganese.  This  cup  replaces  the 
second  metal  plate.  The  liquid  used 
is  a  solution  of  ammonium  chloride 
(sal-ammoniac)  in  water.  This  cell 
is  tolerably  constant  if  it  be  not  used 
to  produce  very  strong  currents,  but 
its  great  merit  is  that  it  is  very  permanent.  It  will  keep 
in  good  condition  for  months  with  very  little  attention, 
furnishing  a  current  for  a  short  time  whenever  wanted. 


FIG.  184. 


VOLTAIC  ELECTRICITY. 


It  is  much  used  for  working  telephones,  electric  bells 
(Fig.  232)  and  clocks,  railway  signals,  etc.  The  man- 
ganese oxide  prevents  polarization  by  destroying  the 
hydrogen  bubbles.  If  the  cell  be  used  continuously  for 
some  time,  its  power  weakens  owing  to  the  accumulation 
of  hydrogen,  but  if  left  to  itself  it  gradually  recovers 
as  the  hydrogen  is  oxidized.  Sometimes  the  manga- 
nese oxide  is  applied  to  the  face  of  the  carbon  and  the 
porous  cup  dispensed  with.  This  cell  has  an  E.  M.  F.  of 
about  1.5  volts.  It  should  be  left  on  open  circuit  when  not 
in  use. 

394.  Daiiiell's  Cell. — This  cell  consists  of  a  copper 
plate  immersed  in  a  saturated  solution  of  copper  sulphate 
(blue  vitriol)  and  a  zinc  plate  immersed  in  dilute  sul- 
phuric acid  or  a  solution  of  zinc  sulphate  (white  vitriol). 
The  two  liquids  are  separated ;  usually 
one  liquid  is  contained  in  a  porous 
cup  placed  in  the  other  liquid.  Cry- 
stals of  copper  sulphate  are  placed  in 
the  solution  of  copper  sulphate  to 
keep  the  lafcter  saturated.  Such  a 
cell  will  furnish  a  nearly  constant 
current,  with  an  E.  M.  F.  of  1.079 
volts  and  keep  in  order  for  a  long 
time.  It  should  be  kept  on  closed  cir- 
cuit when  not  in  use.  The  hydrogen  passes  through  the 
porous  cell  and  acts  upon  the  solution  of  copper  sulphate. 
Copper,  instead  of  hydrogen,  is  deposited  upon  the  copper 
plate.  Polarization  is  thus  avoided.  If  an  incrustation 
forms  near  the  zinc  plate,  remove  some  of  the  solution  of 
zinc  sulphate  and  dilute  what  remains  with  water. 


FIG.  185. 


270 


VOLTAIC   ELECTRICITY. 


(a.)  In  Fig.  186,  the  copper  plate  is  represented  as  a  cleft  cylinder 
within  the  porous  cup,  the  crystals  being  piled  up  around  it.  It  is 
common  to  interchange  the  plates,  the  zinc  heing  in  dilute  sulphuric 
acid  within  the  porous  cup,  and  the  copper  plate  in  the  saturated 
acid  outside  the  porous  cup.  Sometimes  the  outer  vessel  itself  is 
made  of  copper  instead  of  glass  and  serves  as  the  copper  plate  as  is 
shown  in  Fig.  185. 


FIG.  1 86. 


FIG.  187. 


395  The  Gravity  Cell.— This  is  a  modification 
of  the  Daniell's  cell,  no  porous  cup  being  used.  The  cop- 
per plate  is  placed  at  the  bottom  of  the  cell  and  the  zinc 
plate  near  the  top  Crystals  of  copper  sulphate  are  piled 
upon  the  copper  plate  and  covered  with  a  saturated  solu- 
tion of  copper  sulphate.  Water  or,  preferably,  a  weak 
solution  of  zinc  sulphate  rests  upon  the  blue  solution  be- 
low and  covers  the  zinc  plate.  The  two  solutions  are  of 
different  specific  gravities  and  remain  clearly  separated  if 
the  cell  be  kept  on  closed  circuit  when  not  in  use.  (Fig 
187.)  This  cell  is  very  largely  used  in  working  telegraph 
lines.  It  is  sometimes  called  the  Callaud  cell. 

396.  Grove's  Cell. — The  outer  vessel  of  a  Grove's 
cell  contains  dilute  sulphuric  acid.    In  this  is  placed  a 


VOLTAIC  ELECTRICITY. 


271 


hollow  cylinder  of  zinc.  Within  the  zinc  cylinder  is 
placed  a  porous  cup  containing  strong  nitric  acid.  The 
negative  plate  is  a  strip  of  platinum  placed  in  the  nitric 
acid.  The  hydrogen  passes  through  the  porous  cup  and 
reduces  the  nitric  acid  to  nitrogen  peroxide,  which  escapes 
as  brownish-red  fumes.  These  nitrogen  fumes  are  dis- 
agreeable  and  injuribus ;  it  is  well,  therefore,  to  place  the 
battery  in  a  ventilating  chamber  or  outside  the  experiment- 
ing  room.  The  E.  M.  F.  of  the  Grove  cell,  under  favor- 
able conditions,  is  nearly  two  volts,  while  its  internal  re- 
sistance is  small,  being  about  one-fifth  that  of  a  Daniell's 
cell.  It  is  much  used  for  working  induction  coils  (consult 
the  Index),  for  generating  the  electric  light,  etc.  It  is, 
however,  troublesome  to  fit  up  and  should  have  its  liquids 
renewed  every  day  that  it  is  used.  Fig.  189  represents  a 
Grove's  battery  with  cells  joined  in  series. 

397.  Bunsen's  Cell.—     -*»*•>. 

Bunsen's  cell  (Fig.  188)  dif-  | 

fers  from  Grove's  in  the  use  I 

of  carbon  instead  of  expensive 

platinum    for    the    negative 

plate,  thus  reducing  the  cost. 

The   plates  are   made   larger 

than  for  Grove's  battery.     Its 

E.  M.  F.  is  about  the  same  as 

that  of  the  Grove  cell  but  its 

internal  resistance  is  greater.  FIG.  188. 

Fig.  190  represents  a  battery  of  Bunsen's  cells  joined  in 

multiple  arc. 

Note. — There  are  scores  of  different  kinds  of  cells  in  the  market 
competing  for  favor.  Those  here  described  are  among  the  ones 
most  commonly  used. 


272  VOLTAIC  ELECTRICITY. 

398.  A  Voltaic  Battery. — A  number  of  similar 
voltaic  elements  connected  in  such  a  manner  that 
the  current  has  the  same  direction  in  all,  constitutes 
a  voltaic  battery.     The  usual  method  is  to  connect  the 
positive  plate  of  one  element  with  the  negative  plate  of 
the  next,  as  shown  in  Fig.  189.    When  thus  connected, 
they  are  said  to  be  coupled   "tandem"   or  "in   series." 
Sometimes  all  of  the  positive  plates  are  connected  by  a 
wire  and  all  of  the  negative  plates  by  another  wire.     The 
cells  are  then  said  to  be  joined  "  parallel/'  "  abreast "  or 
«in  multiple  arc."     (See  Fig.  190.) 

(a.)  When  two  or  more  cells  are  joined  together,  the  points  of 
Contact  should  be  as  large  as  is  convenient  and  kept  perfectly  clean. 
The  connecting  wire  should  be  of  good  size  and,  for  the  sake  of 
pliability,  a  part  of  it  may  well  be  given  a  spiral  form  by  winding  it 
upon  a  pencil  or  other  small  rod. 

399.  Batteries    of  High    Internal  Resist- 
ance.— Each  kind  of  galvanic  cell  has  an  internal  resist- 


FIG.  189. 

ance,  as  explained  in  §  383.  A  battery  of  cells  joined  in 
series  is  called  a  "battery  of  high  internal  resistance." 
(Fig.  189).  This  method  of  joining  the  cells  increases 


VOLTAIC  ELECTRICITY.  273 

the  length  of  the  liquid  conductor  through  which  the 
current  passes. 

(a.)  In  a  battery  of  cells  joined  in  series,  the  E.  M.  F.  and  the 
internal  resistance  are  those  of  a  single  cell  multiplied  by  the  num- 
ber of  cells.  For  a  circuit  of  great  external  resistance,  a  battery  of 
high  internal  resistance  is  needed. 

4OO.  Batteries  of  Low  Internal  Resist- 
ance.— A  battery  of  cells  joined  parallel  is  called  a 
"battery  of  low  internal  resistance."  (Fig.  190.)  This 
method  of  joining  the  cells  does  not  increase  the  length 
of  the  liquid  conductor  traversed  by  the  current  but  is 
equivalent  to  increasing  its  diameter  or  sectional  area. 

(a.)  In  a  battery  of  cells  joined  parallel,  the  E.  M.  F.  is  that  of  a 
single  cell,  but  the  internal,  resistance  is  that  of  a  single  cell  divided 
by  the  number  of  cells.  For  a  circuit  of  small  external  resistance, 
large  cells,  or  several  cells  joined  parallel,  are  preferable. 


FIG.  190. 

(&.)  A  battery  of  high  internal  resistance  was  formerly  called  an 
intensity  battery,  while  a  battery  of  low  internal  resistance  was 
called  a  quantity  battery. 

4O1.    Requisites    of  a   Good    Battery.— The 

following  conditions  should  be  met  by  a  battery : 

( 1.)  Its  electromotive  force  should  be  high  and  constant, 
(2.)  Its  internal  resistance  should  be  small. 


274  VOLTAIC  ELECTRICITY. 

(3.)  It  should  give  a  constant  current  and,  therefore, 

must  be  free  from  polarization  ;  it  should  not  be 

liable  to  rapid  exhaustion,  requiring  frequent  re- 

newal of  the  acid. 

(4.)  It  should  be  perfectly  quiescent  when  the  circuit 

is  open. 

(  5.)  It  should  be  cheap  and  of  durable  materials. 
(6.)  It  should  be  easily  manageable  and,  if  possible, 

should  not  emit  corrosive  fumes. 

As  no  single  battery  fulfills  all  these  conditions,  some 
batteries  are  better  for  one  purpose  and  some  for  another. 
Thus,  for  telegraphing  through  a  long  line  of  wire  a  con- 
siderable internal  resistance  in  the  battery  is  no  great 
disadvantage  ;  while,  for  producing  an  electric  light,  much 
internal  resistance  is  absolutely  fatal. 

4O2.  The  Best  Arrangement  of  Cells.—  The 
best  method  of  coupling  cells  in  any  given  case  depends 
on  the  work  to  be  done  by  the  battery.  The  maximum 
effect  is  attained  when  the  resistance  of  the  ex- 
ternal circuit  is  made  equal  to  the  internal  resist- 
ance of  the  battery. 

(a.)  For  example,  suppose  that  in  a  given  battery  of  eight  cells  : 

(1.)  Each  cell  has  an  E.  M.  F.  of  two  volts. 

(2.)  Each  cell  has  the  very  high  internal  resistance  of  eight  ohms. 

(3.)  The  battery  is  to  work  through  a  wire  that  has  a  resistance 
of  sixteen  ohms. 

(&.)  First,  couple  the  cells  parallel.  The  E.  M.  F.  of  the  battery 
is  that  of  a  single  cell,  2  volts.  The  internal  resistance  is  8  ohms 
-4-8  =  1  ohm.  Adding  the  external  resistance,  we  have  a  total 
resistance  of  17  ohms.  (See  §  386.) 


This  arrangement  gives  a  current  of  04176+  amperes. 


VOLTAIC  ELECTRICITY.  275 

(<0  Next,  couple  the  cells  in  series.  The  E.  M.  F.  of  the  battery 
is  8  times  2  volts,  or  16  volts.  The  internal  resistance  is  8  times  8 
ohms  or  64  ohms.  Adding  the  external  resistance,  we  have  a  total 
resistance  of  80  ohms. 


. 

This  arrangement  gives  a  current  of  0.2  amperes. 

(d.)  Finally,  join  the  cells  in  two  rows  (each  row  being  a  series 
of  four  cells)  and  join  the  rows  parallel.  The  E.  M.  F.  of  the  battery 
will  be  4  times  2  volts  or  8  volts.  The  internal  resistance  will  be 
4  times  8  ohms  or  32  ohms  for  each  row,  but  only  half  that,  or  16 
ohms,  for  the  whole  battery.  Adding  the  external  resistance,  we 
have  a  total  resistance  of  32  ohms. 

*'p^  ;•-*=!  =i6TT6=°-25-  ;/  -;-;  - 

This  arrangement,  in  which  the  internal  and  the  external  resistances 
are  equal,  gives  a  current  of  0.25  amperes,  the  greatest  possible 
under  the  given  conditions. 

(e.}  A  similar  application  of  Ohm's  law  shows  that  when  the 
external  resistance  is  large,  there  is  little  gain  from  joining  cells 
parallel,  and  thai;  when  the  external  resistance  is  very  smatt,  there  is 
little  gain  in  joining  cells  in  series. 

EXERCISES. 

1.  Given  ten  cells,  each  with  an  electromotive  force  of  1  volt  and 
an  internal  resistance  of  5  ohms.     What  is  the  current  (in  amperes) 
of  a  single  cell,  the  external  resistance  being  0.001  ohm  ? 

Ans.  0.19996+  amperes. 

2.  The  ten  cells  above  mentioned  are  joined  abreast.     The  exter- 
nal resistance  is  0.001  ohm.     What  is  the  current  of  the  battery  ? 

Ans.  1.996+  amperes. 

3.  The  ten  cells  above  mentioned  are  joined  tandem,  the  external 
resistance  remaining  the  same.     What  is  the  current  of  the  battery  ? 

Ans.  0.19999+  amperes. 

4.  What  is  the  current  given  by  one  of  the  above  mentioned  cells 
when  the  external  circuit  has  a  resistance  of  1000  ohms  ? 

Ans.  0.00099502  amperes. 

5.  When  the  ten  cells  are  joined  abreast  with  an  external  resist 
ance  of  1000  ohms,  what  is  the  current  of  the  battery  ? 

Ans.  0.0009995  amperes. 


276  VOLTAIC  ELECTRICITY. 

6.  When  the  ten  cells  are  joined  in  series  with  an  external  resist- 
ance  of  1000  ohms,  what  is  the  current  of  the  battery  ? 

Am.  0.00952  amperes. 

Note. — Compare  the  results  in  Exercises  1,  2  and  3,  where  we 
have  a  small  external  resistance.  Then  compare  the  results  in  Ex- 
ercises 4,  5  and  6,  where  we  have  a  high  external  resistance. 

7.  Why  are  cells  arranged  tandem  for  use  on  a  long  telegraphic 
line? 

8.  What  is  the  resistance  of  2  miles  of  No.  6  electric  light  wire 
(copper  of  ordinary  commercial  quality)?    (See  Appendix  I.) 

Ans.  4.56  ohms. 

9.  A  Brush  dynamo,  No.  8,  will  operate  65  arc  lamps  on  a  short 
circuit.     Each  lamp  has  a  resistance  of  about  4.52  ohms.     If  the 
lamps  be  put  on  a  10  mile  circuit  of  No.  6  copper  wire,  how  many 
lamps  should  be  "  cut  out "  of  the  circuit,  the  dynamo  running  at 
the  same  speed  and  the  current  strength  remaining  the  same  ? 

Ans.  5  lamps. 

10.  Show,  by  a  diagram,  how  a  battery  of  three  cells  should  be 
arranged  when  the  internal  resistance  is  the  principal  one  to  be 
overcome. 

11.  What  is  the  resistance  of  a  mile  of  ordinary  No.  6  iron  tele, 
graph  wire?    (See  Appendix  K,  [2].)  Ans.  13.3  ohms. 

12.  Show  that  the  conductivity  of  water  is  increased  more  than  50 
times  by  adding  half  its  volume  of  sulphuric  acid.     (See  Appendix 
K>  [2].) 

13.  How  much  is  the  conductivity  of  water  increased  by  adding 
^  ite  volume  of  sulphuric  acid  ?  Am.  About  22  times. 


VOLTAIC  ELECTRICITY.  277 

403.  Long  and  Short  Coil  Instruments.— 

A  "long  coil"  galvanometer,  or  a  "long  coil"  electro- 
magnet, or  an  instrument  of  any  kind  in  which  the  con- 
ductor is  a  long,  thin  wire  of  high  resistance,  should  not 
be  employed  on  circuits  the  other  resistances  of  which  are 
small.  Conversely,  on  circuits  of  great  length,  or  where 
there  is  a  high  resistance,  "  short  coil "  instruments  are  of 
little  service  for,  though  they  add  little  to  the  resistances, 
their  few  turns  of  wire  are  not  enough  with  the  small 
currents  that  circulate  in  high-resistance  circuits  ;  "  long 
coil "  instruments  are  here  appropriate,  as  they  multiply 
the  effects  of  the  currents  by  their  many  turns.  Their 
resistance,  though  perhaps  large,  is  not  a  serious  addition 
to  the  existing  resistances  of  the  circuit. 

404.  Divided  Circuits  and  Shunts. — The  cas'e 
of  several  wires  forming  a  multiple  arc  often  occurs  in 
practice.     In  such  cases,  the  current  flowing  in  each 
branch  is    inversely  proportional  to  the  resistance 
of  that  branch.    Either  of  two  such  branches  is  called 
a  shunt.    Evidently,  the  joint  resistance  of  all  the  branches 
is  less  than  the  resistance  of  any  one  of  them. 


FIG.  191. 

(a.)  A  current  flowing  along  a  conductor  divides  at  A,  part  going 
through  a  galvanometer  or  electro-magnet  at  G  and  the  rest  going 
through  the  branch,  B.  The  currents  unite  at  C.  If  the  conductor, 
AGO,  has  a  resistance  of  99  ohms  and  the  conductor,  ABC,  has  a 


278  VOLTAIC  ELECTRICITY. 

resistance  of  1  ohm,  1  per  cent,  of  the  total  current  will  go  through 
G  and  99  per  cent,  will  go  by  way  of  B. 

(6.)  If  we  have  two  wires,  the  separate  resistances  of  which  are 
respectively  28  ohms  and  24  ohms,  placed  abreast  in  a  circuit,  find 
their  joint  resistance.  The  joint  conductivity  will  be  the  sum  of  the 
separate  conductivities  and  conductivity  is  the  reciprocal  of  resist- 
ance. Call  the  joint  resistance  JR. 

-I-J-       JL.=   2t4.^?_^.  7?_??2  no 

R  ~  28        24       672      672  ~  672'  ~  52  ~ 

The  joint  resistance  will  be  12.92  ohms. 

(c.)  The  joint  resistance  of  the  two  branches  of  a  divided  conductor 
is  equal  to  the  product  of  the  separate  resistances  divided  by  their 
sum.  If  there  are  more  than  two  branches,  the  method  employed 
above  may  be  used. 

(d.)  It  is  often  necessary  to  use  a  sensitive  galvanometer  or  other 
instrument  with  a  current  so  strong  that  the  current  would  give  in- 
dications too  large  for  accurate  measurement  or  even  ruin  the  instru- 
ment. Under  such  circumstances,  the  greater  part  of  the  current 
may  be  shunted  around  the  galvanometer.  The  resistance  of  the 
shunt  having  a  known  ratio  to  that  of  the  galvanometer  and  its 
branch,  the  total  current  strength  may  be  computed  from  the  strength 
of  the  current  flowing  through  the  instrument.  Shunt  circuits  may 
be  found  in  almost  all  arc  lamps. 

4O5.  Mechanical  Effects  of  the  Electric 
Current. — The  piercing  of  the  glass  walls  of  an  over- 
charged Leyden  jar  affords  a  good,  though  expensive, 
illustration  of  the  mechanical  effects  of  electricity.  Trees 
and  telegraph  poles  shattered  by  lightning  are  not  un- 
familiar. But,  by  far,  more  important  for  our  considera- 
tion are  the  mechanical  effects  produced  by  voltaic  or 
dynamic  electricity  and,  especially,  the  numerical  rela- 
tion between  the  electricity  used  and  the  work  done. 
This  subject  will  be  considered  in  Section  VI.  of  this 
chapter. 

Experiment  73. — Through  a  long,  thin  platinum  wire,  send  a 
current  that  will  heat  it  to  dull  redness.  Apply  a  piece  of  ice  to  the 


VOLTAIC  ELECTRICITY.  279 

wire  and  notice  that  the  rest  of  the  wire  glows  more  brightly  than  it 
did  before.  Then  heat  a  part  of  the  wire  with  the  flame  .of  a  spirit 
lamp  and  notice  that  the  rest  of  the  wire  glows  less  brightly  than 
before.  In  the  first  case,  the  current  is  strengthened  by  the  in- 
creased conductivity  of  the  cooled  part ;  in  the  second  case,  the  cur- 
rent is  decreased  by  the  increased  resistance  of  the  part  heated  by 
the  lamp. 

Experiment  74.— When  two  curved  metal  surfaces  rest  upon  each 
other,  a  current  passing  from  one  to  the  other  encounters  considera- 
ble resistance  at  the  small  area  of  contact.  The  heat  consequently 
developed  causes  the  parts  in  the  neighborhood  to  expand  very 
quickly  when  the  contact  is  made.  This  often  gives  rise  to  rapid 
vibratory  movements  in  the  conductors.  Gore's  railway  consists  of 
two  concentric  copper  hoops,  whose  edges  are  worked  very  truly 
into  a  horizontal  plane.  A  light  copper  ball  is  placed  on  the  rails 
thus  formed.  One  rail  is  connected  with  the  +  pole  of  a  battery 
of  two  or  three  Grove  cells  and  the  other  rail  with  the  —  pole.  The 
ball  is  then  set  rolling  around  the  track.  If  the  ball  be  true  and  the 
track  well  leveled,  the  energy  supplied  by  the  swelling  (expansion) 
at  the  continually  changing  point  of  contact  is  sufficient  to  keep  up 
the  motion.  The  ball  will  roll  round  and  round,  giving  a  crackling 
sound  as  it  goes. 

Experiment  75. — From  the  poles  of  a  potassium  di-chromate  bat- 
tery, lead  two  stout  copper  wires  and  connect  their  free  ends  by  two 
or  three  inches  of  very  fine  iron  or  platinum  tmre.  Coil  the  iron  wire 
around  a  lead  pencil  and  thrust  a  small  quantity  of  gun-cotton  into 
the  loop  thus  formed.  Plunge  the  zinc  plate  of  the  battery  into  the 
liquid  and  the  iron  wire  will  be  heated  enough  to  explode  the  gun- 
cotton  ;  it  may  be  heated  to  redness  or  even  to  fusion. 

4O6.  Thermal  Effects  of  the  Electric  Cur- 
rent.— Whenever  an  electric  current  flows  through  a 
conductor,  part  of  the  electric  energy  is  changed 
into  heat  energy.  TJie  amount  of  electricity  thus 
changed  into  heat  will  depend  upon  the  amount 
of  resistance  offered  by  the  conductor.  In  the  last 
experiment,  the  stout  copper  wires  were  good  conductors, 
offered  but  little  resistance  and  converted  but  little  of  the 


280  VOLTAIC  ELECTRICITY. 

electrical  energy  into  heat  energy.  The  change  of  ma- 
terial from  copper  to  iron  increased  that  resistance.  This 
increased  resistance  was  again  increased  by  reducing  the 
size  of  the  conductor.  For  this  double  reason,  the  fine 
wire  offered  so  much  resistance  that  a  considerable  of  the 
current  energy  was  transformed  into  heat.  Resistance 
in  an  electric  circuit  always  produces  heat  at  the 
expense  of  the  electric  current.  Thus,  electricity  is 
often  used  in  firing  mines  in  military  operations  and  in 
blasting.  All  known  metals  have  been  melted  in  this  way, 
while  carbon  rods  have  been  heated  by  a  battery  of  600 
Bunsen's  elements  until  they  softened  enough  for  welding. 
By  means  of  a  Leyden  jar  battery  and  a  universal  dis- 
charger, remarkable  thermal  effects  may  be  obtained. 
Houses  are  sometimes  set  on  fire  by  lightning.  The  nu- 
merical relations  between  electricity  and  heat  are  con- 
sidered in  Section  VI.  of  this  chapter. 


4O7.  Luminous  Effects  of  the  Electric 
Current. — The  electric  spark,  the  glow  seen  when  elec- 
tricity escapes  .from  a  pointed  conductor  in  the  dark  and 
the  various  forms  of  lightning  are  some  of  the  now 
familiar  luminous  effects  of  electricity.  Whenever  an 
electric  circuit  is  closed  or  broken,  there  is  a  spark  at  the 
point  of  contact,  due  to  the  heating  of  a  part  of  the  con- 
ductor to  incandescence.  We  have  seen  luminous  effects 
produced  by  winding  the  wire  from  one  plate  of  a  voltaic 
cell  round  one  end  of  a  file  and  drawing  the  other  electrode 
along  the  side  of  the  file,  thus  rapidly  closing  and  break- 
ing the  circuit.  If  the  iron  wire  used  in  the  last  experi- 
ment was  heated  sufficiently,  it  also  gave  a  luminous  effect 


VOLTAIC  ELECTRICITY.  281 

and  illustrated  the  fundamental  principle  of  the  incandes- 
cence electric  lamp  (§  466). 

(a.)  The  most  important  luminous  effects  of  electricity  will  be 
considered  in  connection  with  dynamo-electric  machines  (§  465).  It 
will  be  noticed  that  all  of  these  are  secondary  thermal  effects. 

4O8.  Galvani's  Experiment.— In  1786,  Galvani, 
a  physician  of  Bologna,  noticed  convulsive  kicks  in  a 


FIG.  192. 

frog's  legs  when  acted  upon  by  an  electric  current.  A  frog 
was  killed  and  the  hind  limbs  cut  away  and  skinned,  the 
crural  nerves  and  their  attachments  to  the  lumbar  vertebrae 
remaining.  Two  dissimilar  metals  were  held  in  contact  and 
their  free  ends  brought  into  contact  with  nerve  and  muscle 
respectively,  as  shown  in  Fig.  192.  Convulsive  muscular 
contractions  brought  the  legs  into  a  position  similar  to 


282  VOLTAIC  ELECTRICITY. 

that  represented  by  the  dotted  lines  in  the  figure.  A  frog's 
legs  thus  prepared  make  a  very  sensitive  galvanoscope. 
It  is  said  that  they  show  even  the  very  feeble  induction 
currents  of  the  telephone,  though  the  best  galvanometers 
barely  detect  them. 

4O9.  Physiological  Effects  of  the  Electric 
Current. — An  electric  current  may  produce  muscular 
convulsions  in  a  recently  killed  animal.  Experiments 
with  the  Leyden  jar  and  the  induction  coil  show  that 
similar  effects  may  be  produced  upon  the  living  animal. 
The  "  electric  shock,"  which  is  physiological  in  its  nature, 
is  familiar  to  most  persons.  The  sensation  thus  produced 
cannot  be  described,  forgotten  or  produced  by  any  other 
agency. 

Electricity  is  largely  used  as  an  agent  for  the  cure  of 
disease;  experiments  of  this  kind  may  do  injury  and 
would  better  be  left  to  the  educated  physician.  The  dis- 
charge of  a  large  battery  may  be  fatal  and  a  number  of 
persons  have  lost  their  lives  within  the  last  few  years  by 
coming,  accidentally  or  otherwise,  into  the  circuit  of  a 
dynamo-electric  machine.  Interrupted  and  alternating  cur- 
rents are  more  serious  in  their  physiological  effects  than 
continuous  currents. 

(a.)  If  the  members  of  a  class  form  a  chain  by  joining  hands,  the 
first  member  holding  a  feebly -charged  Leyden  jar  by  its  outer  coat 
and  the  last  member  touching  the  knob,  a  simultaneous  shock  will 
be  felt  by  each  person  in  the  chain.  A  similar  experiment  may  be 
made  with  a  Ruhmkorff  coil.  A  single  Leyden  jar  has  been  dis- 
charged through  a  regiment  of  1500  men,  each  soldier  receiving  a 
shock.  Dr.  Priestley  killed  a  rat  with  a  battery  of  seven  feet  of 
coated  surface,  and  a  cat  with  a  battery  of  forty  feet  of  coated 
surface. 


VOLTAIC  ELECTRICITY.  283 

Experiment  76. — Into  a  bent  tube  (known  to  dealers  in  chemical 
glassware  as  a  TJ  tube),  put  a  solution  of  any 
neutral  salt,  e.  g.,  sodium  sulphate.  Color  the 
contents  of  the  tube  with  the  solution  from 
purple  cabbage.  In  the  arms  of  the  tube,  place 
the  platinum  electrodes  of  a  battery,  as  shown  in 
Fig.  193.  Close  the  circuit  and  presently  the 
liquid  at  the  +  electrode  will  be  colored  red  and 
that  at  the  —  electrode,  green.  If,  instead  of 
coloring  ths  solution,  a  strip  of  blue  litmus  paper 
be  hung  near  the  +  electrode  it  will  be  reddened, 
while  a  strip  of  reddened  litmus  paper  hung  near  FIG.  193. 

the   —  electrode  will   be  colored    blue.      These 
changes  of  color  are  chemical  tests;  the  appearance  of  the  green  or 
blue  denotes  the  presence  of  an  alkali  (caustic  soda  in  this  case), 
while  the  appearance  of  the  red  denotes  the  presence  of  an  acid. 

Experiment  77. — Melt  some  tin  and  pour  the  melted  metal  slowly 
into  water.  Dissolve  some  of  this  granulated  tin  in  hot  hydrochloric 
acid  and  add  a  little  water.  Into  this  bath  of  a  dilute  solution  of 
tin  chloride,  introduce  two  platinum  electrodes  from  a  battery  of  a 
few  cells.  A  remarkable  growth  of  tin  crystals  will  shoot  out  from 
the  —electrode  and  spread  towards  the  +,  bearing  a  strong  resem- 
blance to  vegetable  growth.  Hence,  it  is  called  the  "  tin  tree." 
Repeat  the  experiment  with  solutions  of  lead  acetate  ("sugar  of 
lead  ")  and  of  silver  nitrate. 

41O.  Chemical  Effects  of  the  Electric  Cur- 
rent.— The  electric  spark  may  be  made  to  produce  chem- 
ical combination  or  chemical  decomposition.  Ammonia 
(NH3),  or  carbon-dioxide  (C03),  may  be  decomposed  by 
passing  a  series  of  sparks  through  it.  A  mixture  of  oxygen 
and  hydrogen  may  be  caused  to  enter  into  chemical  union 
by  the  electric  spark,  the  product  of  the  union  being  water. 
(See  Chemistry,  Exp.  53.)  Many  chemical  compounds 
may  be  decomposed  by  passing  the  current  through  them. 
The  compound  must  be  in  the  liquid  condition,  either  by 
solution  or  by  fusion.  Substances  that  are  thus  decom- 
posed are  called  electrolytes ;  the  process  is  called 


284 


VOLTAIC  ELECTRICITY. 


trolysis ;  the  compound  is  said  to  be  electrolyzed.  The 
electrolysis  of  acidulated  water  is  easily  accomplished  with 
a  current  from  three  or  four  Grove's  or  Bunsen's  cells. 
The  water  is  decomposed  into  oxygen  and  hydrogen.  The 
apparatus,  shown  in  Fig.  194,  may  be  called  a  water- 
voltameter. 


FIG.  194. 

(a.)  The  apparatus  consists  of  a  vessel  containing  water  (to  which 
a  little  acid  has  been  added  to  increase  its  conductivity)  in  which 
are  immersed  two  platinum  strips  that  constitute  the  two  elec- 
trodes of  a  battery.  When  the  circuit  is  closed,  bubbles  of  oxygen 
escape  from  the  positive  electrode  and  bubbles  of  hydrogen  from 
the  negative.  The  gases  may  be  collected  separately  by  inverting, 
over  the  electrodes,  tubes  filled  with  water,  as  shown  in  the  figure. 
The  volume  of  hydrogen  thus  collected  will  be  about  twice  as  great 
as  that  of  the  oxygen. 

(6.)  A  water- voltameter  may  be  made  by  cutting  off  the  bottom  of 
a  wide-mouthed  glass  bottle  (Chemistry,  App.  4,  h.)  and  passing  two 
insulated  wires,  varnished  and  terminating  in  platinum  strips, 
through  a  cork  that  closes  the  mouth  of  the  inverted  bottle.  Two 
test  tubes  will  complete  the  instrument.  When  a  sufficient  quantity 
of  the  gases  has  been  collected,  they  may  be  tested  ;  the  hydrogen, 
by  bringing  a  lighted  match  to  the  mouth  of  the  test  tube,  where- 
upon the  hydrogen  will  burn ;  the  oxygen,  by  thrusting  a  splinter 


VOLTAIC  ELECTRICITY.  xJ85 

with  a  glowing  spark  into  the  test  tube,  whereupon  the  splinter  will 
kindle  into  a  flame. 

(e.)  Each  coulomb  of  electricity  liberates  0.1176  cu.  cm.  of  hydrogen 
and  0.0588  cu.  cm.  of  oxygen,  or  a  total  of  0.1764  cu.  cm.  of  the 
mixed  gases.  The  electrolysis  of  9  g.  of  water  requires  95,050 
coulombs. 

411.  Ions. — The  products  of  electrolysis,  like  the  oxy- 
gen and  hydrogen,  are  called  ions;  the  one  that  goes  to 
the  +  electrode  (or  anode)  is  called  the  anion;  the  one 
that  goes  to  the  —  electrode  (kathode  or  cathode)  is  called 
the  Icathion  or  cathion. 

(a.)  The  amount  of  chemical  action  in  a  cell  is  proportional  to  the 
strength  of  current  while  it  passes.  One  coulomb  of  electricity,  in 
passing  through  a  cell,  liberates  0.0000105  gram  of  hydrogen  and 
dissolves  0.00034125  gram  of  zinc. 

(&.)  One  coulomb  will  cause  the  deposition  of  0.0003307  gram  of 
copper.  To  deposit  1  gram  of  copper  requires  3024  coulombs.  This 
principle  has  been  used  in  the  Edison  meter  for  electric  lighting 
purposes,  a  certain  proportion  of  the  current  being  shunted  through 
a  "  copper  voltameter  "  or  bath  of  copper  sulphate  solution,  as  de- 
scribed in  the  next  experiment. 

Experiment  78. — From  the  +  pole  of  a  voltaic  battery  or  dy- 
namo-electric machine,  suspend  a  plate  of  copper  ;  from  the  —  pole, 


FIG.  195. 

suspend  a  silver  coin.     Place  the  copper  and  silver  electrodes  in  a 
strong  solution  of  copper  sulphate  (blue  vitriol).     When  the  circuit 


286  VOLTAIC  ELECTRICITY. 

is  closed,  the  salt  of  copper  is  electrolyzed,  the  copper  from  the  salt 
being  deposited  upon  the  silver  coin  and  the  sulphuric  acid  going  to 
the  copper  or  +  electrode.  The  silver  is  thus  electro-plated  with 
copper.  (Fig.  195.) 


412.  Electro -Metallurgy.  —  The  many  applica- 
tions of  this  process  of  depositing  a  metallic  coat  on  a 
body  prepared  for  its  reception,  constitute  the  important 
art  of  electro-metallurgy.  If,  with  the  apparatus  used  in 
the  last  experiment,  a  solution  of  some  silver  salt  be  used 
instead  of  the  copper  sulphate  solution  and  the  direction 
of  the  current  be  reversed,  silver  will  be  deposited  upon 
the  copper  plate,  which  will  thus  be  silver-plated.  If  the 
positive  electrode  be  a  plate  of  gold  and  the  bath  a  solu- 
tion of  some  salt  of  gold  (cyanide  of  gold  dissolved  in  a 
solution  of  cyanide  of  potassium),  gold  will  be  deposited 
upon  the  copper  of  the  negative  electrode,  which  will  be 
thus  electro-gilded.  In  electrotyping,  impressions  of  type 
or  engravings  are  taken  in  wax,  or  any  other  plastic  ma- 
terial that  is  impervious  to  water.  A  conducting  surface 
is  given  to  such  a  mould  by  brushing  finely  powdered 
graphite  over  it ;  it  is  then  placed  in  a  solution  of  sulphate 
of  copper  facing  a  copper  plate.  The  mould  is  then  con- 
nected with  the  —  pole  of  a  dynamo  or  a  vol  taic  battery  and 
the  copper,  with  the  -f-  pole;  when  the  current  passes 
through  the  bath,  copper  will  be  deposited  upon  the  mould. 
When  the  copper  film  is  thick  enough  (say  as  thick  as  an 
ordinary  visiting  card),  it  is  removed  from  the  mould  and 
strengthened  by  filling  up  its  back  with  melted  type- 
metal.  The  copper  film  and  the  type-metal  are  made  to 
adhere  by  means  of  an  amalgam  of  equal  parts  of  tin  and 
lead.  The  copper-faced  plate  thus  produced  is  an  exact 


VOLTAIC  ELECTRICITY.  287 

reproduction  of  the  type  and  engravings  from  which  the 
mould  was  made. 

(a.)  In  all  these  cases,  the  metal  is  carried  in  the  direction  of  the 
current  and  deposited  upon  the  negative  electrode.  In  electro- 
plating and  gilding,  the  technicalities  of  the  art  refer  chiefly  to  the 
means  of  making  the  deposit  firmly  adherent.  In  electrotyping, 
they  refer  chiefly  to  the  preparation  of  the  mould  or  matrix. 

413.  Electro-Chemical  Series.— The  facts  just 
considered   suggest    a   division   of    substances    into   two 
classes,   electro-positive   and  electro- negative.      Tlie    ion 
that  goes  to  the  negative  electrode  is  called  electro- 
positive;  that  which  goes  to  the  positive  electrode 
is  called  electro-negative. 

(a.)  Kathions  are  called  electro-positive  because  they  seem  to  be 
attracted  to  the  negative  pole  of  the  battery  (kathode),  the  idea  be- 
ing that  of  attraction  between  opposite  electricities.  Hydrogen  and 
the  metals  are  kathions  or  electro-positive.  They  seem  to  move  with 
the  current,  going  as  far  as  possible  and  being  deposited  where  the 
current  leaves  the  "  bath "  or  electrolytic  cell.  Similarly,  anions 
are  said  to  be  electro-negative. 

414.  The  E.  M.  F.  of  Polarization.— The  prod- 
ucts of  electrolysis  have  a  tendency  to  reunite  by  virtue 
of  their  chemical  affinity.     (Chemistry,  §  8.)     For  exam- 
ple, the  electrolysis  of  zinc  sulphate  gives  zinc  and  sul- 
phuric acid.     But  we  now  well  know  that  the  chemical 
action  of  these  two  substances  has  an  electro-motive  force 
of  its  own.     This  E.  M.  F.  of  the  ions  acts  in  opposition 
to  that  of  the  electrolyzing  current.     In  some  cases,  it 
rises  higher  than  the  E.  M.  F.  of  the  original  current  and 
reverses  the  direction  of  the  current.     The  oxygen  and 
hydrogen,  yielded  by  the  electrolysis  of  water,  tend  to  re- 
unite and  set  up  an  opposing  E.  M.  F.  of  about  1.45  volts. 


288  VOLTAIC  ELECTRICITY. 

Thus  we  see  that  it  requires  a  battery  or  cell  with  an  E. 
M.  F.  of  more  than  1.45  volts  to  decompose  water.  This 
electro-motive  force  of  the  ions  is  called  the  E.  M. 
F.  of  Polarization.  It  may  be  observed  by  putting  a 
galvanometer  in  the  place  of  the  battery  of  the  water- 
voltameter  (Fig.  194).  The  polarization  in  a  voltaic  cell 
acts  in  the  same  way. 

(a.)  There  is  no  opposing  E.  M.  F.  of  polarization  when  the  kathion 
and  the  anode  are  of  the  same  metal.  For  example,  the  feeblest 
current  will  deposit  copper  from  a  solution  of  copper  sulphate,  when 
ihe  anode  is  a  copper  plate. 

Experiment  79. — Suspend  two  strips  of  bright  sheet  lead  facing 
each  other  in  dilute  sulphuric  acid.  Pass  a  current  through  these 
plates  by  connecting  them  with  a  battery  of  4  or  5  cells  in  series.  A 
dark  peroxide  of  lead  will  form  on  one  of  the  bright  plates.  Then 
remove  the  battery  and,  in  its  place,  put  a  short  coil  galvanometer  or 
electro-magnet.  It  will  be  found  that  the  lead-plate  cell  is  supply- 
ing a  current,  the  direction  of  which  is  the  reverse  of  the  charging 
battery  previously  used. 

415.  Secondary  Batteries. — When  a  voltameter 
or  an  electro-plating  bath  is  supplying  a  current  of  elec- 
tricity, as  mentioned  in  the  last  paragraph,  it  constitutes 
a  secondary  battery.  As  the  ions  do  not  reunite  when  the 
circuit  is  open,  the  energy  of  the  decomposing  current 
may  be  stored  up  as  energy  of  chemical  affinity.  When 
a  current  is  again  wanted,  the  circuit  may  be 
closed  and  the  energy  of  chemical  affinity  at  once 
appears  as  energy  of  electric  current.  Secondary 
batteries  are,  consequently,  often  called  storage 
batteries. 

(a.)  The  Faure  battery  consists  of  two  plates  of  sheet  lead  coated 
with  red  lead  (lead  sesqui-oxide,  Pb804).  These  plates  are  septi- 


VOLTAIC   ELECTRICITY.  289 

rated  by  a  layer  of  paper  or  cloth,  rolled  up  in  a  loose  coil  like  a  roll 
of  carpet  and  immersed  in  dilute  sulphuric  acid. 

(b.)  When  a  current  from  a  dynamo-electric  machine  or  a  voltaic 
battery  is  sent  through  such  a  cell,  chemical  action  is  produced. 
Oxygen  acts  on  the  coating  of  the  anode  plate  and  converts  it  into  a 
higher  oxide  of  lead  (the  peroxide,  PbO2).  Hydrogen  acts  upon 
the  coating  of  the  kathode  plate  and  reduces  it  to  metallic  lead  in  a- 
spongy  condition.  When  these  changes  have  gone  as  far  as  possi- 
ble, the  battery  is  said  to  be  '•  charged."  The  charged  plates  will 
remain  in  this  condition  for  days  if  the  circuit  be  left  open. 

(c,)  By  closing  the  circuit,  the  plates  will,  at  any  time,  furnish  a 
current  until  they  are  changed  to  their  original  chemical  condition. 
As  the  lead  plates  and  the  acid  are  not  rapidly  destroyed,  the  battery 
may  be  charged  and  discharged  many  times. 


FIG. 


(d.)  Many  serious  defects  in  the  Faure  battery  have  been  obviated 
in  the  Brush  battery  (Fig.  196).  These  batteries  are  composed  of  a 
number  of  cells  containing  cast  lead  plates  of  a  peculiar  construction, 
electro-chemically  prepared  and  immersed  in  dilute  sulphuric  acid. 
These  cells  may  be  connected  together,  tandem  or  abreast,  so  as  to 
produce  any  desired  result.  A  large  number  of  these  batteries  may 
be  placed  in  one  circuit  and  charged  by  the  current  of  one  dynamo.  It 
will  thus  be  seen  that  the  dynamo  may  be  made  to  do  double  duty, 
charging  batteries  by  day  for  use  in  connection  with  the  incandes- 
cence lamps  and  supplying  arc  lamps  direct,  at  night.  The  E.  M.  F. 


290  VOLTAIC  ELECTRICITY. 

of  each  Brush  cell  is  about  two  volts.  For  electric  lighting,  they 
are  generally  prepared  in  batteries  of  twenty  or  more  cells.  An 
automatic  current  "  manipulator "  or  switch  is  provided  with  each 
Brush  battery  and  is  arranged  so  as  to  retain  the  battery  in  circuit 

until  it  is  charged  and 
then  to  disconnect  it  from 
the  circuit.  When  the 
charge  has  been  exhausted 
to  a  certain  point,  it  brings 
the  battery  into  the  cir- 
cuit again  and  holds  it  till 
it  has  been  recharged  and 
then  cuts  it  out  as  before. 
The  same  operation  is  re- 
peated with  every  battery 
in  circuit.  The  operation 
is  automatic.  Each  bat- 
tery has  a  clock  attached, 
which  registers  the  time 
thaf;  the  charging  current 
has  been  passing  through 
FlG-  T97-  the  cells.  The  incandes- 

cence lamps  are  connected  with  the  batteries  through  the  "  manipu- 
lator," as  shown  in  Fig.  197.  The  quantity  of  electricity  capable 
of  being  "stored"  may  be  increased  by  increasing  the  number  of 
cells  and  the  size  of  the  plates. 

416.  Magnetic  Effects  of  the  Electric  Cur- 
rent.— Any  conductor  is  rendered  magnetic  by  passing 
a  current  of  electricity  through  it.  A  common  needle 
may  be  magnetized  by  winding  about  it  an  insulated  cop- 
per wire  and  discharging  a  Leyden  jar  through  the  wire. 
We  have  already  seen  that  a  bar  of  soft  iron  may  be  tem- 
porarily magnetized  by  the  influence  of  the  voltaic  current. 
It  may  be  further  shown  by  the  action  of  the  bar  and 
helix. 

(a.)  This  apparatus  consists  of  a  movable  bar  of  soft  iron  surrounded 
by  a  coil  of  insulated  copper  wire  (Fig.  198).  When  the  wire  of  the 
coil  is  placed  in  the  closed  circuit  of  a  battery,  the  iron  bar  becomes 


VOLTAIC  ELECTRICITY. 


291 


FIG.  198. 


strongly  magnetized ;  when  the  circuit  is  broken,  the  bar  instantly 

loses  its  magnetic  power.      The  bar  may  be  a 

straight  piece  of  stout  iron  wire  ;  the  helix  may 

be  made  by  winding  insulated  copper  wire  upon 

a  piece  of  glass  tubing  large  enough  to  admit 

the  wire  and  not  quite  as  long  as  the  iron. 

(&.)  A  good  helix,  convenient  for  many  pur- 
poses, may  be  made  upon  an  ordinary  wooden 

spool.     With  a  sharp  knife,  make  the  shank  of 

the  spool  as  thin  as  possible  and  then  wind  the 

spool  full  of  insulated  copper  wire  about  as  large  as  ordinary  broom 

or  stove-pipe  wire.      The  iron  bar  must  be  small  enough  to  pass 

easily  through  the  hole  in  the  spool  and  long  enough  to  project  a 

little  ways  beyond  each  end. 

(c.)  Either  of  these  helices  may  be  placed  in  the  circuit  of  a  cell 

and  held  in  a  vertical  position,  when  it  will  act  as  a  "  sucking " 

magnet.     The  movable  iron  core  will  be  held  in  mid-air  "  without 

any  visible  means  of  support." 

(d.)  The  "  helix  and  ring  armature  "  is  shown  in  Fig.  199.  The 
armature  is  of  soft  iron  divided  into  two  semicircles 
with  brass  handles.  When  the  helix  is  placed  in  a 
closed  circuit,  the  semicircles  resist  a  considerable 
force  tending  to  draw  them  apart ;  when  the  circuit 
is  broken,  they  fall  asunder  of  their  own  weight. 
The  iron  ring  may  be  made  without  handles  by  any 
blacksmith.  Stout  cords  will  answer  for  handles. 
The  helix  may  be  made  by  winding  insulated  wire 
upon  a  pasteboard  cylinder  an  inch  or  an  inch  and  a 
half  long  There  should  be  four  or  five  layers  of 
stout,  copper  wire  which  may  be  tied  together  with 

strings  passing  through  the  hole  in  the  helix. 
(e.)  Such  temporary  magnets  as  these  are  called  electro-magnets. 

The  subject  of  electro-magnets  will  be  further  considered  in  §§  442- 

448. 


FIG.  199. 


417.  Deflection  of  the  Magnetic  Needle.— 

We  have  already  seen  that  the  voltaic  current  has  a 
marked  effect  in  turning  the  magnetic  needle  from  its  north 
and  south  position,  tending  to  place  the  needle  at  right 
angles  to  the  direction  of  the  current.  This  may  be  easily 
shown  by  Oersted's  apparatus  represented  in  Fig.  200.  It 


292  VOLTAIC  ELECTRICITY. 

consists  of  a  magnetic  needle  and  a  brass  wire  frame  with 
three  pole-cups,  permitting  the  current  to  be  passed  over, 
under,  or  around  the  magnet.  The 
space  immediately  surround- 
ing a  wire  carrying  an  electric 
current  is  a  field  of  magnetic 
force  as  truly  as  is  the  space 
around  a  magnetized  body 
(§  433). 

Flo.  200.  (a.)  If  the  current  pass  above  the  needle 

from  north  to  south,  the  north-seeking  or 

—  end  of  the  magnet  will  be  deflected  toward  the  east ;  if  it  pass 
from  south  to  north,  the  —  end  of  the  needle  will  be  deflected  toward 
the  west.  If  the  current  pass  below  the  needle,  the  deflections  will 
be  the  opposite  of  those  just  mentioned.  The  wires  are  insulated 
where  they  cross  at  a. 

418.  The  Astatic  Galvanometer. — This  gal- 
vanometer depends  upon  the  principles  set  forth  in  the 
last  paragraph.  It  is  a  very  delicate  instrument  for 
detecting  the  presence  of  an  electric  current  and 
determining  its  direction  and  strength.  In  Oersted's 
apparatus,  the  needle  is  heavy  and  a  considerable  force  is 
needed  to  set  it  in  motion  ;  in  the  galvanometer,  the  needle 
is  very  light  and  suspended  so  as  to  turn  easily.  In  Oersted's 
apparatus,  the  needle  is  held  in  the  magnetic  meridian  by 
the  directive  influence  of  the  earth  ;  in  the  galvanometer, 
this  is  obviated  almost  wholly  by  the  use  of  an  astatic  needle 
(§  439).  In  Oersted's  apparatus,  the  current  makes  but  a 
single  course  about  the  needle  ;  in  the  galvanometer,  the 
wire  is  insulated  and  coiled  many  times  about  the  needle ; 
thus  the  effect  is  multiplied.  One  of  the  needles  is  within 
the  coil  while  the  other  swings  above  it,  the  two  being 
connected  by  a  vertical  axis  passing  through  an  appro- 


VOLTAIC  ELECTRICITY.' 


293 


FIG.  201. 


priate  slit  in  the  coil.  If  both  needles  were  within  the 
coil,  since  their  poles  are  reversed,  the  same  current  would 
tend  to  deflect  them  in  opposite  directions  and  thus  the 
action  of  one  needle  would  neutralize 
that  of  the  other.  The  astatic  needle 
is  suspended  by  an  untwisted  silk 
fibre  from  a  hook  which  may  be  low- 
ered when  the  instrument  is  not  in 
use  until  the  upper  needle  rests  upon 
the  dial  plate  beneath  it.  The  ends 
of  the  coiled  wire  are  connected  with 
binding  screws ;  leveling  screws  are 
provided,  by  means  of  which  the  in- 
strument may  be  adjusted  so  that  the 
needles  shall  swing  clear  of  all  obstructions.  A  glass 
cover  protects  from  dust  and  disturbance  by  air  currents. 
The  instrument  is  represented  in  Fig.  201. 

(a.)  When  the  deflections  of  tlie  astatic  galvanometer  are  less  than 
10°  or  15°,  they  are  very  nearly  proportional  to  the  strengths  of  the 
currents  that  produce  said  deflections.  A  current  that  deflects  the 
needle  6°  is  about  three  times  as  strong  as  one  that  deflects  it  2°. 

(&.)  That  a  galvanometer  shall  be  good,  it  must  be  able  to  meas- 
ure the  strength  of  the  current  in  some  certain  way.  It  must  be 
adapted  to  the  currents  to  be  measured  by  it.  A  galvanometer  fitted 
for  the  measurement  of  small  currents  (e.  g.,  five  or  six  milliamperes) 
would  not  be  suitable  for  measuring  a  ten  ampere  arc  electric 
light  current.  If  the  current  to  be  measured  has  passed  through 
a  circuit  of  great  resistance  (e.  g.,  several  miles  of  telegraph  wire), 
a  short  coil  galvanometer  consisting  of  only  a  few  turns  of  wire  will 
not  answer;  a  long-coil  galvanometer,  with  many  turns  of  wire 
about  the  needle,  must  be  used.  Hence,  it  will  be  seen  that  differ- 
ent kinds  of  galvanometers  are  needed  for  different  kinds  of  work. 
(See  Appendix  L.) 

Experiment  80. — Connect  an  iron  and  a  German  silver  wire  to 
the  binding  posts  of  a  sensitive,  short-coil,  astatic  galvanometer. 
Twist  the  free  ends  of  the  wires  together  and  heat  the  junction  in 


294  •  THERMO-ELECTRICITY. 

the  flame  of  an  alcohol  lamp.  The  deflection  of  the  galvanometer- 
needle  will  show  that  an  electric  current  is  traversing  the  circuit. 
Cool  the  junction  with  a  piece  of  ice.  The  galvanometer  will  show 
that  a  second  current  is  flowing  in  the  opposite  direction. 

419.  Thermo-Electricity.  —  //   a    circuit    be 
made  of  two  metals  and   one  of  the  junctions  be 
heated   or   chilled,  a  current  of  electricity   is   pro- 
duced. 

(a.)    This  may   be   further  illustrated  by  the  apparatus   shown 

in  Fig.  202.  The 
upper  bar,  m  n, 
having  its  ends 
bent,  is  made  of 
copper ;  the  low- 
er, op,  is  of  bis- 
muth. This  rect- 
angular frame  is 
to  be  placed  in  the 
magnetic  merid- 
ian and  a  mag- 
n  et  ic  needle 
placed  within  it. 
FIG.  202.  Upon  heating  one 

of  the  junctions, 

a  current  will  be  produced,  the  existence  of  which  is  satisfactorily 
shown  by  the  deflection  of  the  needle  as  indicated  in  the  figure.  The 
junction  may  be  chilled  with  a  piece  of  ice  or  by  placing  upon  it 
some  cotton  wool  moistened  with  ether.  In  this  case,  a  current, 
opposite  in  direction  to  the  first,  will  be  produced ;  the  needle  will 
be  turned  the  other  way.  The  frame  may  be  simplified  by  bend- 
ing a  strip  of  copper  twice  at  right  angles  to  make  the  top,  bottom 
and  one  end  of  the  frame,  the  other  end  being  a  cylinder  of  bis- 
muth. But  the  form  shown  in  Fig.  202  is  preferable,  as  the  same 
junction  may  be  heated  by  the  lamp  below  or  chilled  by  laying  a 
piece  of  ice  on  the  upper  side. 

420.  A    Thermo-electric  Pair.— If   a   bar  of 

antimony,  A,  be  soldered  to  a  bar  of  bismuth,  B,  and  the 
free  ends  joined  by  a  wire,  we  evidently  have  a  circuit 


THERMO-ELECTRICITY. 


equivalent  to  the  one  considered  in  the  last  paragraph. 
When  the  junction,  (7,  is  heated,  a  current  will  pass,  from 
bismuth  to  antimony  across  the  junction  and  from  anti- 
mony to  bismuth  through  the  wire,  as  shown  in  Fig.  203. 

(a.)  The  arrangement  is  analogous  to  a  voltaic  element,  the 
antimony  representing  the  —  plate  and 
carrying  the  +  electrode,  the  bismuth  rep- 
resenting the  +  plate  and  carrying  the  — 
electrode,  while  the  solder  takes  the  place 
of  the  liquid.  The  E.  M.  F.  of  an  antimony- 
bismuth  pair  for  1°  C.  difference  of  temper- 
ature is  about  117  microvolts.  Just  as  a  number  of  voltaic  elements 
may  be  connected,  so  may  a  number  of  thermo-electric  pairs  be 
connected  to  form  a  thermo-electric  series. 


421.  The  Thermo-electric  Pile.  —  Several 
thermo-electric  pairs,  generally  five,  six,  or  seven,  are 
arranged  in  a  vertical  series,  as  shown  in  Fig.  204,  the 
intervening  spaces  being  much  reduced,  the  successive 
bars  separated  by  strips  of  varnished  paper  only  and  the 
wire  connection  omitted.  A  similar  series  may  be  united 
to  this  by  soldering  the  free  end  of  the  antimony  bar  of 
one  series  to  the  free  end  of  the  bis- 
muth bar  of  the  other,  the  two  series 
being  separated  by  a  strip  of  varn- 
ished paper.  Any  desirable  number 
of  such  series  may  be  thus  united, 
compactly  insulated  and  set  in  a 
metal  frame  so  that  only  the  sold- 
ered ends  are  open  to  view.  The  free  end  of  the  antimony 
bar,  representing  the  -f  electrode,  and  the  free  end  of 
the  bismuth  bar,  representing  the  -*  electrode,  are  con- 
nected with  binding  screws,  whicfh  may  be  connected  with 
a  sensitive  short-coil  galvanometer.  The  thermo-electric 


296 


THERMO-ELECTRICITY. 


pile,  with  the  addition  of  conical  reflectors,  is  shown 
in  Fig.  205.  A  change  of  temperature  at  either  exposed 
face  of  the  pile  produces  a  feeble  current  of  electricity 
which  is  manifested  by  the  movement  of  the  needle  of  the 

galvanometer.  The  instrument 
is  much  used  in  scientific  work 
for  detecting  differences  in  tem- 
perature, being  much  more 
'  sensitive  than  the  mercury  ther- 
mometer. 


FIG.  205. 


423.  The  Peltier  Ef- 
fect.— When  .an  electric  cur- 
rent passes  over  a  junction 
from  antimony  to  bismuth, 
there  is  an  evolution  of  heat  at 
the  junction,  the  temperature 
of  which  rises.  When  the  current  passes  in  the  op- 
posite direction  (from  bismuth  to  antimony),  there  is  an 
absorption  of  heat  and  the  temperature  of  the  junction 
falls.  In  other  words,  if  the  current  be  sent  through  the 
circuit  in  the  direction  in  which  the  thermo-electromotive 
force  would  naturally  send  it,  the  heated  junctions  will  be 
cooled  and  the  cooled  junctions  will  be  heated. 


EXERCISES. 

1.  (a.)  Draw  a  figure  of  a  simple  voltaic  element.     (6.)   State 
what  is  meant  by  the  electric  current,     (c.)   Indicate,  upon  the 
figure,  the  direction  of  the  current,     (d.)  What  are  the  electrodes  ? 
(e.)  Indicate  them  by  their  proper  signs  upon  the  figure. 

2.  (a.)  Describe  or  figure  a  high  resistance  battery  of  Grove's  ele- 
ments.    (&.)  A  low  resistance  battery  of  Bunsen's  elements,     (c.) 
What  is  the  peculiar  advantage  of  the  Daniell's  battery  ? 


VOLTAIC  AND    THERMO-ELECTRICITY.  297 

3.  Describe  an  experiment  illustrating  the  heating  effects  of  cur- 
rent electricity. 

4.  (a.)  How  may  a  very  feeble  current  be  detected  ?    (&.)  Describe 
the  apparatus  used,     (c.)  Mention  the  features  contributing  to  its 
delicacy. 

5.  (a.)  If  the  resistance  of  one  mile  of  a  certain  electric  light  wire 
is  3.58  ohms,  what  is  the  resistance  of  4.4  miles  of  the  same  wire? 
(6.)  The  resistance  of  a  certain  wire  is  5  ohms  per  100  yd.     What 
length  of  the  same  wire  will  have  a  resistance  of  13.2  ohms? 

Ans.  (a.)  15.75  ohms.     (&.)  264  yd. 

6.  What  is  the  resistance  of  a  mile  of  copper  wire  that  has  a 
diameter  of  65  mils  if  the  resistance  of  a  mile  of  copper  wire  80  mils 
in  diameter  is  8.29  ohms  ?  Ans.  12-56  ohms. 

7.  If  the  resistance  of  700  yd.  of  a  certain  wire  is  0.91  ohm,  what 
is  the  resistance  of  1,320  yd.?  Ans.  1.72  ohm. 

8.  (a.)  Define  electrolyte.     (6.)  What  term  is  applied  to  chemical 
decomposition  when  effected  by  means  of  an  electric  current?    (c.) 
How  would  you  go  about  the  task  of  determining  for  yourself  the 
electro-chemical  nature  of  a  substance  ? 

9.  The  resistance  of  a  certain  wire  is  4.55  ohms.     The  resistance 
of  a  mile  of  the  same  wire  is  1.3  ohms.     What  is  the  length  of  the 
first  wire  ?  Ans.  3.5  mi. 

10.  The  resistance  of  a  mile  of  copper  wire  70  mils  in  diameter  is 
10.82  ohms.     What  is  the  diameter  of  a  copper  wire  a  mile  long  and 
having  a  resistance  of  23  ohms  ?  Ans.  0.048  inch  or  48  mils. 

11.  What  should  be  the  length  of  a  silver  wire  so  that  it  may 
have  the  same  resistance  as  10  inches  of  copper  wire  of  the  same 
thickness,  the   conductivity  of  silver  being  1.0467  times  that  of 
copper  ? 

12.  Find  the  resistance,  at  the  freezing  temperature,  of  20  m.  of 
German  silver  wire  weighing  52.5  grams,  having  given  that  the  resist- 
ance, at  the  same  temperature,  of  a  wire  of  the  same  material  1  m. 
long  and  weighing  1  g.  is  1.85  ohms.  Ans.  14.1  ohm. 

13.  When  a  piece  of  fine  platinum  wire  and  a  galvanometer  are 
put  in  the  circuit  of  a  galvanic  cell,  the  needle  is  deflected.     Remove 
the  platinum   wire  and  close  the   circuit  with  stout  copper  wire  ; 
the  needle  is  deflected  more  than  before.     Explain. 

14.  Find   the   resistance  of  500  yd.  of  copper  wire  165  mils  in 
diameter,  the  resistance  of  one  mile  of  copper  wire  230  mils  in 
diameter  being  one  ohm.  Ans.  0.55  ohm. 

15.  If  1,000  ft.  of  wire  95  mils  in  diameter  have  a  resistance  of 
1.15  ohm,  what  is  the  diameter  of  a  wire  of  the  same  material  that 
has  a  resistance  of  10.09  ohms  per  1,000  ft.?  Ans.  32  mils. 


298 


VOLTAIC  AND   THERMO-ELECTRICITY. 


16.  Under  what   circumstances  is  it  desirable  to  arrange  cells 
as  shown  in  Fig.  206  ? 

17.  A  copper  wire  6  m.  long  has  a  diameter  of  0.74  mm.     What 
is  the  length  of  a  copper  wire  of  1  mm.  diameter  that  has  the  same 

electrical  resistance  ?  Ans.  10.957  m. 

18.  Given  8  cells,  each  with  an  E.  M.  F.  of  2  volts 
and  an  internal  resistance  of  8  ohms.     The  resistance 
of  the  external  circuit  is  to  be  16  ohms.     How  shall 
the  cells  be  arranged  to  give  maximum  current  and 
what  will  that  current  be?  Ans.  0.25  ampere. 

19.  What  is  the  length  of  an  iron  wire  having  a 
sectional  area  of  4  sq.  mm.  and  the  same  resistance  as 
a  copper  wire  1,000  yd.  long,  the  latter  having  a  sec- 
tional area  of   1  sq.  mm.,  the   conductivity   of  iron 
being  |-  that  of  copper?  Ans.  571  f  yd. 

20.  Two  incandescence  lamps  of  31  and  37  ohms 
respectively  are  placed  abreast  in  a  circuit.    Find  the 
joint  resistance  of  the  two  lamps.    Ans.  16.87  ohms. 

21.  How  thick  must  an  iron  wire  he  so  that  it  and 
a  copper  wire  that  has  the  same  length  and  a  diame- 
ter of  2.5  mm.  shall  have  the  same  resistance,  the  re- 

FIG.  206.         sistance  of  iron  being  7  times  that  of  copper? 

Ans.  6.61  mm. 

22.  How  many  coulombs  will  be  furnished  by  the  consumption  of 
20  g.  of  zinc  ? 

23.  What  weight  of  zinc  must  be  consumed  in  each  cell  of  a 
voltaic  battery  of  3  Daniell's  cells  to  enable  the  electrolysis  of  9  g. 
of  water?    (Neglect  loss  by  local  action.)  Ans.  About  32.5  #. 

24.  What  weight  of  copper  will  be  deposited  in  each  cell  of  the 
battery  mentioned  in  the  last  problem?  Ans.  About  31.5  g. 

25.  Three  wires,  the  respective  resistances  of  which  are  5,  7  and 
9  ohms  are  joined  in  multiple  arc.     Find  the  resultant  resistance  of 
this  compound  conductor.  Ans.  2.2  ohms. 

26.  What  is  the  necessary  E.  M.  F.  of  a  dynamo  that  is  to  furnish 
a  10  ampere  current  for  60  arc  lamps  (in  series),  each  of  which  has  a 
resistance  of  4.5  ohms,  the  resistance  of  the  line  wire  being  10  ohms 
and  the  internal  resistance  of  the  dynamo  being  22  ohms  ? 

27.  A  piece  of  zinc,  at  the  lower  end  of  which  a  piece  of  copper 
wire  is  fixed,  is  suspended  in  a  glass  jar  containing  a  solution  of 
acetate  of  lead  (sugar  of  lead).     After  a  few  hours,  a  deposit  of  lead 
in  tree-like  form  grows  downward  from  the  copper  wire.     Explain 
this.  ,.;.•-: 

28.  Liquids  increase  in  conductivity  with  an  increase  of  temper- 


VOLTAIC  AND   THERMO-ELECTRICITY.  299 

ature.     Will  a  given  battery  give  a  stronger  current  at  0°  C.  or  at 
20°  C.? 

29.  What  should  be  the  length  of  a  lead  wire  so  that  it  may  have 
the  same  resistance  as  10  inches  of  copper  wire  of  the  same  thickness, 
the  conductivity  of  lead  being  0.0923  times  that  of  copper  ? 

30.  Four  wires  are  joined  together  in  multiple  arc,  their  resist- 
ances being  5.5,  18,  3.7  and  2.9  ohms  respectively.    Find  the  result 
ant  resistance  of  the  compound  conductor  thus  formed. 

Ans.  1.17  ohm. 


HONORARY   PROBLEM. 

31.  Find  the  number  of  incandescence  lamps  that  may  be  worked 
in  multiple  arc  by  a  dynamo-electric  machine  that  has  an  internal 
resistance  of  0.032  ohm.  The  E.  M.  F.  of  the  dynamo  is  55  volts 
and  the  resistance  of  each  lamp  is  28  ohms.  The  current  must  be 
1.6  amperes  in  each  lamp.  Ans.  199  lamps. 


300 


VOLTAIC  AND   THERMO-ELECTRICITY. 


Recapitulation.— To  be  amplified  by  the  pupil  for 
review. 


Smee's. 

'  One  Liquid.  .  • 

Potassium 
di-chromate. 

Leclanche. 

Daniell's. 

CEL-.            H 

Two  Liquids.  • 

Callaud's. 
Grove's. 

Bunsen's. 

\ 

Tandem. 

Joined.  - 

Abreast. 
Best  Method. 

r  VOLTAIC  - 

SOURCE  OF  ENERGY. 

(  High  Internal  Resistanct. 
BATTERY.  .  .  •<  Low  Internal  Resistance. 

\  Requisites. 

CURRENT..  . 

Direction 
Strength  • 

Unit. 
Ohm's  Law, 

1  ^ 

1  SIMPLE. 

0 

CIRCUIT  - 

DIVIDED. 

SHUNT. 

PLATE. 

POLE. 
ELECTRODE. 

A  node. 
Kathode. 

o 

POTENTIAL  ; 

FALL  OF  E. 

M    F    j  Unit. 
'  |  Measurement. 

J>H 

s 

'  EXTERNAL. 

t^^ 

C—  i 

111 

INTERNAL. 

G 

X 
o 

RESISTANCE  . 

LAWS. 
••  '    UNIT. 

MEASURE 

WENT. 

2 

LONG  AND  SHORT-COIL  INSTRUMENTS. 

PH 

QUANTITY  • 

UNIT. 

u 

(    r*  .  ... 

w 

LOCAL  ACTION.  -J  £JJJj£y 

a- 

L  POLARIZATION.  j  R£MEEDV. 

^ 

f  MECHANICAL 

jgj 

THERMAL;.... 

RELATION  TO  RESISTANCE. 

w 

LUMINOUS. 

f  ELECTROLYSIS,  -j  jj£&£ 

,  h°ns- 

* 

£ 

PHYSIOLOGICAL.      ELECTRO.METALLURGV":'" 

P5 

r^ 

o 

CHEMICAL... 

..  .  •    ELECTRO-CHEMICAL  SERIES. 

** 

Ul 

E.    M.   F.   OF   POLARIZA- 

u. 

TION. 

f  Faure's. 

u. 

Ul 

SECONDARY  BATTERIES.. 

\  Brush's. 
\   Uses. 

\  Advantages, 

MAGNETIC.  .  . 

(  ELECTRO-MAGNETS. 
.  .  -<  ELECTRIC  TELEGRAPH. 

(  GALVANOMETER. 

TUCDMn    Cl   COTOI/MTV 

(For  Induced  Currents^  see  Section  V.  of  this  Chapter.) 


iv. 


MAGNETISM. 


Natural  Magnets. — One  of  the  most  valua- 
ble iron  ores  is  called  magnetite  (Fe3  04).  Occasional 
specimens  of  magnetite  will  attract  filings  and  other  pieces 
of  iron.  Such  a  specimen  is  called  a  lodestone. 
It  is  a  natural  magnet. 

424.  Artificial  Magnets. — Artificial  magnets  are 
either  temporary  or  permanent.      A  temporary  magnet 
is  usually  made   of  soft  iron  and   is  called  an  electro- 
magnet.    A  permanent  magnet  is  usually  made  of  steel. 
Artificial   magnets  have  all  the 

properties    of    natural    magnets 
and  are  more  powerful  and  con- 
venient.     They    are,   therefore,  FIG.  207. 
preferable  for  general  use.    The 

most  common  forms  are  the  straight  or  "bar  magnet  and 
the  horseshoe  magnet.  The  first  of  these  is  a  straight  bar 
of  iron  or  steel;  the  second  is  shaped  like  a  letter  U,  the 
ends  being  thus  brought  near  together,  as  shown  in  Fig. 
207.  A  piece  of  iron  placed  across  the  two  poles  of  a 
horseshoe  magnet  is  called  an  armature.  We  have  already 
learned  how  to  make  artificial  magnets. 

425.  Reteiitivity. — It  is  more  difficult  to  get  the 
magnetism  into  steel  than  into  iron.    It  is  also  more  dim*- 


302 


MAGNETISM. 


cult  to  get  it  out.  This  power  of  resisting  magneti- 
zation or  demagnetization  is  called  coercive  force 
or  retentivity.  The  harder  the  steel,  the  greater  its  re- 
tentivity.  Soft  wrought  iron  has  but  little  retentivity. 

426.   Distribution   of  Magnetism.— If  a  ba* 

magnet  be  rolled  in  iron  filings  and  then  withdrawn,  the 


FIG.  208. 

filings  cling  to  the  ends  of  the  bar  but  not  to  the  middle. 
This  form  of  attraction  is  not  evenly  distributed  through- 
out the  bar.  It  is  greatest  at  or  near  the  ends. 
These  points  of  greatest  attraction  are  called  the 
poles  of  the  magnet.  It  is  impossible,  by  any  known 
means,  to  develop  one  magnetic  pole  without  simultane- 


MAGNETISM.  303 

ously  developing  another  pole  of  opposite  sign.  The  mid- 
dle of  the  magnet  does  not  attract  iron  and  is  called  the 
equator  or  neutral  point. 

Experiment  81. — Bring  either  end  of  a  bar  magnet  near  the  end 
of  a  floating  piece  of  iron,  AB  ;  the  iron  is 
attracted.  Bring  the  same  end  of  the 
magnet  near  the  middle  of  the  iron  ;  the 
iron  is  attracted.  Bring  the  same  end  of 
the  magnet  near  the  other  end  of  the  iron  ; 
the  iron  is  attracted.  Repeat  the  experi- 
ments with  the  other  end  of  the  magnet ; 
in  each  case,  the  iron  is  attracted.  FIG. 

427.  Attraction   between   a   Magnet    and 

Iron. — ^Either  pole  of  a  magnet  will  attract  or- 
dinary iron. 

Experiment  82.— Freely  suspend  three  bar  magnets,  A,  B  and  C, 
at  some  distance  from  each  other.  This  may  be  done  by  placing  each 
magnet  in  a  stout  paper  stirrup  supported  by  a  cord  or  horse-hair  or 
upon  a  board  or  cork  floating  on  water.  (See  Fig.  209.)  When  they  have 
come  to  rest,  each  will  lie  in  a  north  and  south  line.  Magnets  for  this 
experiment  may  be  made  by  magnetizing  (§  448)  three  stout  knitting- 
needles.  If  there  is  any  electric  light  apparatus  in  your  neighbor- 
hood in  charge  of  a  good-natured  man,  he  will  probably  magnetize 
the  needles  for  you.  Each  needle  may  be  suspended  by  means  of  a 
triangular  piece  of  stiff  writing-paper.  Pass  the  needle  through  the 
paper  near  the  lower  corners  ;  at  the  other  corner,  affix,  by  wax,  the 
end  of  a  horse-hair.  The  poles  may  be  indicated  by  little  bits  of  red 
and  of  white  paper,  fastened  by  means  of  wax  to  the  ends  of  the 
needles.  Mark  the  north -seeking  poles,  —  and  the  south-seeking 
poles,  +. 
I  > 

428.  Characteristics    of  Magnets. — Magnets 
are  chiefly  characterized  by  the  property  of  attract- 
ing iron   and   by  a   tendency  to  assume  a   partic- 
ular direction  of  position  when  freely  suspended. 

Experiment  83. — (a.)  Take  magnet  A  of  Experiment  82  from  its 


304 


MAGNETISM. 


support  and  bring  its  +  end  near  the  —  end  of  B  or  C.  Notice  the 
attraction. 

(b.)  Bring  the  +  end  of  A  near  the  +  end  of  B  or  G.  Notice  the 
repulsion. 

(c.)  Bring  the  —  end  of  A  near  the  —  end  of  B  or  G.  Notice  the 
repulsion. 

(d.)  Bring  the  —  end  of  A  near  the  +  end  of  B  or  C.  Notice  the 
attraction. 

(e.)  From  («.),  we  learned  that  the  —  ends  of  B  and  G  were  each 
attracted  by  the  +  end  of  A.  Bring  the  —  end  of  B  near  the  — 
end  of  C.  Notice  that  they  now  repel. 

(/.)  From  (&.),  we  learned  that  the  +  ends  of  B  and  G  were  each 
repelled  by  the  +  end  of  A.  Bring  the  +  end  of  B  near  the  +  end 
G.  Notice  that  they  now  repel. 

(g.)  In  similar  manner,  show  that  the  +  end  of  B  will  attract  the 
-  end  of  C',  that  the  —  end  of  B  will  attract  the  +  end  of  G. 

Record  the  results  of  your  experiments  in  tabular  form  thus; 


(a.)  +  attracts  — . 
(d.)  —  attracts  +. 
etc. 


(b.)  +  repels  +. 
(c.) .—  repels  — . 
etc. 


Experiment  84. — Magnetize  a  number  of  fine  sewing-needles  by 
drawing  the  +  end  of  a  bar  magnet  three  or  four  times  from  the  eye 
^____^^  to  the  point  of  each. 

Cut  several  small 
corks  into  slices 
about  an  eighth  of 
an  inch  thick. 
Through  each  cork 
disc,  push  a  needle 
up  to  its  eye,  point 
downward,  and 
place  them  in  a 
round  dish  of  water. 
These  little  mag- 1 
nets  have  their  like 

poles  presented  to  each  other  and  they  mutually  repel.  Bring  the 
bar  magnet,  with  its  +  end  downward,  over  the  needles  ;  they  will 
be  driven  to  the  sides.  Similarly,  bring  the  —  end  over  them  ;  they 
will  be  attracted  toward  the  centre. 


FIG.  210. 


429.    Laws   of  Magnets.— (1.)    Every    magnet 


MAGNETISM.  305 

has  two  similar  poles;  like  poles  repel  each  other', 
unlike  poles  attract  each  other. 

(2.)  Magnetic  force,  like  other  forms  of  attrac- 
tion and  repulsion,  varies  inversely  as  the  square 
of  the  distance. 

Experiment  85. — Dip  one  of  the  magnetized  knitting-needles  into 
iron  filings.  Notice  that  filings  cling  to  the  ends,  near  the  paper 
discs,  but  that  none  cling  to  the  middle.  Break  the  needle  in  the 
middle  and  dip  each  piece  into  iron  filings.  Notice  that  the  un- 
marked ends,  which  were  at  the  middle  of  the  unbroken  magnet, 
now  attract  iron  filings  as  well  as  do  the  marked  ends.  Poles  have 
been  developed  in  parts  of  the  needle  that  previously  showed  no  mag- 
netic attraction. 

43O.  Effect    of  Breaking   a   Magnet.— If   a 

magnet  be  broken,  each  piece  becomes  a  magnet  with  two 
poles  and  an  equator  of  its  own.  These  pieces  may  be 
repeatedly  subdivided  and  each  fragment  will  be  a  perfect 
magnet. 


It  is  probable  that  every  jnolecule  has  its  poles 
or  is  polarized  and  that,  could  one  be  isolated,  it 
would  be  a  perfect  magnet.  We  may,  thus,  conceive 
a  magnet  as  made  up  of  molecules  each  of  which  is  a 
magnet,  the  action  of  the  molar  magnet  being  due  to  the 
combined  action  of  all  the  molecular  magnets  of  which  it 
is  composed. 

431.  Magnetized,  Magnetic  and  Diamag- 
lietic  Substances, — A  magnetized  body  is  one  that 


306  MAGNETISM. 

can  be  made  to  repel  a  pole  of  a  freely  suspended  magnet 
Substances  that  are  attracted  by  a  magnet  are  called  mag- 
netic; e.g.,  iron  or  steel  and  nickel.  Substances  that  are 
repelled  by  a  magnet  are  called  diamagnetic  ;  e.g.,  bismuth, 
antimony,  zinc,  tin,  mercury,  lead,  silver,  copper,  gold 
and  arsenic.  Of  these,  iron  is  by  far  the  most  magnetic, 
while  bismuth  is  the  most  diamagnetic.  The  magnetic 
properties  of  iron  or  steel  are  easily  shown ;  diamagnetic 
properties  require  a  powerful  magnet  for  satisfactory  illus- 
tration. 

Experiment  86.— Wrap  a  bar  magnet  in  a  piece  of  cloth.  With 
it,  attract  and  repel  the  poles  of  a  suspended  magnet. 

Experiment  87. — Repeat  the  last  experiment,  holding  a  slate  or 
sheet  of  zinc  between  the  two  magnets. 

Experiment  88.— Put  one  piece  of  the  broken  magnet  into  a  bot- 
tle ;  cork  the  bottle  tightly.  With  it,  attract  and  repel  the  poles  of 
a  suspended  magnet. 

432.  Magnetic  Screens. — Nothing  but  a  mag- 
netic body  can  cut  off  the  inductive  action  of  a 
magnet.  If  a  small  magnet  be  suspended  inside  a  hol- 
low iron  ball,  no  outside  magnet  will  affect  it. 

Experiment  89. — With  the  end  of  a  good  bar  magnet,  write  your 
name  upon  the  blade  of  a  handsaw.  The  invisible  characters  may 
be  made  visible  by  sifting  fine  iron  filings  upon  the  blade. 

Experiment  90. — Place  a  piece  of  card-board  or  rough  drawing 
paper  over  a  good  bar  magnet.  Sift  fine  iron  filings  through  a  piece 
of  muslin  upon  the  card-board  and  tap  it  lightly.  The  iron  particles 
will  move  and  arrange  themselves  in  well  defined  curved  lines.  (See 
Fig.  212.)  By  using  two  bar  magnets  placed  side  by  side,  first,  with 
like  poles  near  each  other  and,  secondly,  with  unlike  poles  near  each 
other,  their  combined  effect  on  the  iron  filings  may  be  easily  ob 
served.  The  figures  will  be  widely  different. 


MAGNETISM. 


307 


4:33.  Magnetic  Field. — A  maguet  seems  to  be  sur- 
rounded by  an  atmosphere  of  magnetic  influence  called 
the  magnetic  field.  (See  §  450^  and  Appendix  N.) 
The  magnetic  curves,  formed  in  the  above  experiment, 
are  very  interesting  and  instructive  for  they  show  the 
direction  of  the  lines  of  magnetic  force.  The  filings 
in  any  one  of  these  curves  are  temporary  magnets  with 


FIG.  212.  •/« 

adjoining  poles  opposite  and  therefore  attracting.  If  a 
small  magnetic  needle  be  suspended  over  the  card  board 
at  any  point,  its  length  will  tend  to  lie  in  the  direction 
of  the  lines  of  magnetic  force  at  that  point  as  mapped  out 
by  the  iron  filings. 

(a.)  The  figures  may  be  permanently  fixed  by  using  a  sheet  of 
glass  that  has  been  gummed  and  dried,  instead  of  the  sheet  of 
paper.  Tlie  filings  are  sifted  evenly  over  the  surface  ;  then  the  glass 
is  tapped ;  then  a  jet  of  steam  is  caused  to  play  gently  above  the 
sheet,  softening  the  surface  of  the  gum,  which,  as  it  hardens,  fixes 
the  filings  in  their  places. 

(6.)  Since  the  lines  of  force  are  made  of  little  magnetic  particles 
that  set  themselves  thus  in  obedience  to  the  attractions  and  re- 
pulsions in  the  field,  they  represent  the  resultant  direction  of  said 
forces  at  each  point.  They  map  out  the  magnetic  field,  showing  the 
f]irection  of  the  magnetic  force  by  their  position  and  its  intensity  b^ 


308  MAGNETISM. 

their  number.  If  a  small  —  pole  could  be  obtained  alone  and  put 
down  on  any  one  of  these  lines  of  force,  it  would  tend  to  move  along 
that  line  from  +  to  —  ;  a  single  +  pole  would  tend  to  move  along 
the  line  in  an  opposite  direction. 

Experiment  91. — Rub  one  end  of  a  steel  pen  against  the  end  of  a 
magnet.  Dip  the  pen  into  iron  filings  and  notice  that  the  newly 
made  magnet  has  a  pole  at  each  end.  Determine  the  sign  of  each  of 
these  poles,  as  indicated  in  Experiment  82. 

434.  Magnetization   by  Contact. — A  bar  of 

iron  or  steel  may  be  magnetized  by  rubbing  it 
against  a  magnet.  Pure  or  soft  iron  is  easily  magnet- 
ized but  quickly  loses  its  magnetism  when  the  magnetiz- 
ing influence  is  removed.  Hardened  steel  is  magnetized 
with  more  difficulty  but  retains  its  magnetism  after  the 
removal  of  the  magnetizing  influence. 

Experiment  92. — Move  the  point  of  an  unmagnetized  steel  pen  to 
and  fro  very  near  one  end  of  a  magnet  but  without  touching  it  to 
the  magnet.  Dip  the  pen  into  iron  filings  and  determine  whether 
or  not  it  has  been  magnetized.  Tf  it  has,  determine  the  sign  of  each 
pole,  as  in  the  last  experiment  and  notice  whether  the  point  of  the 
pen  is  of  the  same  polarity  as  the  end  of  the  magnet  near  which  it 
was  moved. 

Experiment  93. — Bring  a  short  bar  of  soft  iron,  I,  very  near  a 
strong  bar  magnet,  M,  end  to  end,  as  shown  in  the  figure.  Sprinkle 


FIG.  213. 

iron  filings  over  the  ends  of  the  iron  bar  and  they  will  cling  as  they 
would  to  a  magnet.  The  iron  bar  is  a  magnet,  while  it  remains  in 
this  position. 

435.  Magnetic  Induction. — If  the  end  of  a  bar 

of  soft  iron  be  brought  near  one  of  the  poles  of  a  strong 


MAGNETISM. 


magnet,  the  iron  becomes,  for  the  time  being,  a  mag- 
net.  The  poles  of  the  temporary  magnet  will  be  opposite 
to  those  of  the  permanent  magnet,  i.e.,  if  the  -f  or  posi- 
tive pole  of  the  magnet  be  presented  to  the  iron  bar,  it 
will  develop  a  —  or  negative  pole  in  the  nearest  end  of  the 
iron  bar  and  a  +  pole  at  the  further  end.  Bring  the  iron 
bar  nearer  the  magnet  and  this  effect  will  be  increased. 
Actual  contact  is  not  necessary,  but  when  the  iron  and 
the  magnet  touch,  the  magnetizing  force  is  the  greatest. 
If  a  steel  bar  be  used  instead  of  an  iron  bar,  it  will  be  per- 
manently instead  of  temporarily  magnetized.  The  iron 
or  the  steel  is  induced  to  become  a  magnet  by  the 
influence  of  the  rnaguet  used.  It  is  said  to  be 
magnetized  by  induction.  This,  like  other  forms  of 
attraction,  varies  inversely  as  the  square  of  the  distance. 
We  have  already  seen  that  magnetic  induction  takes  place 
in  certain  directions  called  lines  of  magnetic  force 
(§  433.) 

Experiment  94. — Bring  a  soft  iron  ring  to  the  end  of  a  magnet. 
It  will  be  supported.     Bring  a  second  ring  into  contact  with  the 
first  ring  and  it  will  be  sup- 
ported.    In  this  way,  quite 
a  number  of  rings  may  be 
supported,  each  ring  being 
magnetized  by   the  bar  or 

ring  magnet  above  it.     Of  FIG.  214. 

course,  the  attractive  force 

is  continually  weakening  from  the  first  to  the  last  ring.  Sup- 
port the  upper  ring  upon  your  finger  and  remove  the  magnet. 
Each  ring  ceases  to  be  a  magnet  and  the  chain  is  broken  into 
its  separate  links.  Vary  the  experiment  by  using,  instead  of 
the  rings  :  (1,)  Soft  iron  nails  ;  (2,)  Steel  sewing- needles ;  and 
see  if  there  is  any  difference  in  the  results. 

Experiment  95. — Suspend  an  iron  key  from  the  positive  end  of 
a  bar  magnet.     The  key  is  inductively  magnetized,  the  relation  of 


310 


MAGNETISM. 


its  poles  to  each  other  and  to  the  magnet  being  as  shown  in  Fig. 
215.  A  second  bar  magnet  of  about  the  same  power,  with  its  poles 
opposite,  is  moved  along  the  first  magnet.  When  the  —  end  of  the 
second  magnet  comes  over  the  key,  the  key  drops. 


FIG.  215. 

The  first  magnet  tends  to  induce  a  -  pole  at  the  upper  end  of  the 
key.  The  second  magnet  tends  to  induce  a  +  pole  at  the  same 
point.  The  effect  of  each  magnet  neutralizes  that  of  the  other. 

Experiment  96. — Magnetize  a  piece  of  watch  spring  about,  six 
inches  long  (easily  obtainable  at  the  watch  repairer's)  by  drawing  it 
several  times  between  the  thumb  and  the  end  of  a  magnet.  Dip  it 
into  iron  filings.  Lift  it  carefully  with  its  load.  Bring  the  poles  of 
t'.ie  spring  magnet  together,  bending  the  magnet  into  a  ring.  The 
magnet  drops  its  load. 

436.  Induction  Precedes  At- 
traction.— We  now  see  why  a  magnet 
attracts  ordinary  iron;  it  first  magnetizes 
it  and  then  attracts  it.  The  attraction  be- 
tween unlike  poles  is  greater  than  the  re- 
pulsion between  like  poles  because  of  the 
smaller  distance  between  them.  Compare 
§336. 

Experiment  97. — Test  a  common  fire  poker  for 
magnetism  by  bringing  a  small  magnetic  needle  near 
its  ends  and  seeing  whether  the  poker  repels  either 
pole  of  the  compass  needle  or  whether  the  two  ends  of  the  poker 
attract  different  poles  of  the  needle.    If  the  poker  is  not  even  slightly 
magnetic,  place  it  with  its  upper  end  sloping  toward  the  south  so  as 


MAGNETISM.  311 

to  make  an  angle  of  a  little  less  than  half  a  right  angle.  In  other 
words,  place  it  in  the  position  assumed  by  the  dipping  needle. 
(§  439.)  While  the  poker  is  in  this  position,  strike  it  a  few  blows 
with  a  wooden  block  or  mallet.  Test  it  again  for  magnetism.  A 
steel  poker  that  has  usually  stood  in  a  nearly  vertical  position  may, 
thus,  often  be  shown  to  have  acquired  magnetism. 

437.  The  Earth  is  a  Magnet.— The  earth  acts 
like  a  huge  magnet  in  determining  the  direction  of  com- 
pass and  dipping  needles.  Its  inductive  influence,  as 
shown  in  the  last  experiment,  strengthens  the  belief  that 
it  has  such  action.  If  a  small  dipping  needle  be  placed 
over  the  —  end  of  a  bar  magnet,  the  needle  will  take  a 
vertical  position  with  its  -f  end  down.  As  the  needle  is 
moved  toward  the  other  end  of  the  bar,  it  turns  from  its 


FIG.  217. 

vertical  position.  When  over  the  neutral  line,  the  needle 
is  horizontal.  As  it  approaches  the  +  end  of  the  magnet, 
the  needle  again  becomes  vertical,  but  the  —  end  of  the 
needle  is  drawn  down.  If  a  dipping  needle  be  carried 
from  far  southern  to  far  northern  latitudes,  it  will  act  in  a 
similar  way.  Many  facts  seem  to  teach  that  the  earth  is 
a  great  magnet  with  magnetic  poles  near  its  geo- 
graphical poles.  The  magnetic  pole  in  the  northern 
hemisphere  was  found  in  1832  by  Capt.  Ross.  It  was  then 
a  little  north  and  west  of  Hudson's  Bay,  in  latitude 


312  MA  GNETfSM. 

70°  05'  N.,  and  longitude  96°  45'  W.  A  place  in  the  south- 
ern hemisphere  has  been  found  where  the  dipping  needle 
is  nearly  vertical. 

438.  Names  of  Magnetic  Poles. — We  have  now  learned 
to  regard  the  earth  as  a  huge  magnet,  with  one  pole  in  the  northern 
hemisphere  and  one  in  the  southern.      Since  unlike  poles  attract 
each  other,  it  follows  that  the  earth's  magnetic  pole  situated  in  the 
northern  hemisphere  is  opposite,  in  kind,  to  the  end  of  a  magnetic  needle 
that  points  to  the  north.     From  this  fact,  great  confusion  of  nomen- 
clature has  arisen.     We  have  spoken  of  the  end  of  the  needle  that 
points  north  as  —  or  negative.     Following  this  nomenclature,  the 
northern  magnetic  pole  of  the  earth  must  be  +  or  positive.      But 
popular  usage  calls  the  north -seeking  end  of  the  needle  the  north 
pole  and  the  other  end  the  south  pole.     This  introduces  great  confu- 
sion when  we  wish  to  speak  of  the  magnetic  poles  of  the  earth. 
The  nomenclature  that  we  have  adopted  obviates  this  confusion. 

Experiment  98. — Make  a  horizontal  needle  of  a  piece  of  watch 
spring  about  six  inches  long  and  straightened  by  drawing  it  between 
thumb  and  finger.     Heat  the  middle  of  the 
needle  to  redness  in  a  flame  and  bend  it 
double.      Bend  the  ends  back  into  a  line 
with   each  other,   as   shown   in  Fig.   218. 
Magnetize  each  end  separately  and   oppo- 
FIG.  218.  sitely.      Wind  a  waxed  thread  around  the 

short  bend  at  the  middle  to  form  a  socket 

and  balance  the  needle  upon  the  point  of  a  sewing-needle  thrust  into 
a  cork  for  support.  A  little  filing,  clipping  with  shears  or  loading 
with  wax  may  be  necessary  to  make  it  balance.  The  needle  will 
point  north  and  south. 

Experiment  99. — By  means  of  a  fine  wire  fork,  gently  lay  one  of 
the  magnetized  sewing-needles  of  Experiment  84  on  the  surface  of 
water.  It  will  float  without  any  cork  or  similar  support  and  will 
assume  a  north  and  south  position.  It  may  be  considered  the  needle 
of  a  small  compass. 

439.  Magnetic  Needles.—.^  small  bar  magnet 
suspended   in   such    a    manner    as   to    allow    it   to 
assume   its  chose n   position  is  a  magnetic  needle. 
It  may  turn  in  a  horizontal  or  a  vertical  plane. 


MAGNETISM. 


313 


FIG  219. 


(a.)  If  it  be  free  to  move  in  a  horizontal  plane,  it  is  a  horizontal 
needle ;  e.  g.,  the  mariner's  or  the  survey- 
or's compass  (Fig.  219).  It  will  come  to 
rest  pointing  nearly  north  and  south. 
If  the  magnet  be  free  to  move  in  a  ver- 
tical plane,  it  constitutes  a  vertical  or 
dipping  needle  (Fig.  220).  Two  magnets 
fastened  to  a  common  axis  but  having 
their  poles  reversed  constitute  an  astatic 
needle  (Fig.  221).  An  astatic  needle  as- 
sumes no  particular  direction  with  respect 
to  the  earth  if  the  two  needles  are  equally 
magnetized.  (§  418.) 

(&•)  Make  a  dipping  needle  by  thrusting  a  knitting-needle  through 

a  cork  so  that  the  cork  shall  be  at 
the  middle  of  the  needle.  Thrust 
through  the  cork,  at  right  angles 
to  the  knitting-needle,  half  a  knit- 
ting-needle, or  a  sewing-needle, 
for  an  axis.  Support  the  ends  of 
the  axis  upon  the  edges  of  two 
glass  goblets  or  other  convenient 
objects.  Push  the  knitting-needle 
through  the  cork  so  that  it  will 
balance  upon  the  axis  like  a  scale- 
beam.  Magnetize  the  knitting- 
needle  and  notice  the  dip. 

(c.)  A  magnetized  sewing- 
needle,  suspended  near  its  middle 
(at  its  centre  of  gravity)  by  a  fine 
thread  or  hair  or  an  untwisted 
fibre  will  serve  as  a  dipping  needle. 
It  should  first  be  suspended  so  as  to  hang  + 
horizontal  and  magnetized  afterward. 
A  simple  form  of  dipping  needle  is  repre-  - 
sented  in  Fig.  222. 


FIG.  220. 


44O.  Inclination  or  Dip. — 

The    angle     that     a     dipping 
needle    makes    with    a     hori- 
zontal   line    is    called    its    in-  FIG.  221. 
elination  or  dip.      The  angle  in  question  is  indicated 


314 


MAGNETISM. 


by  the  dotted  arc  of  Fig. 


FIG.  222. 
masked  by  the  effect  of  gravity. 


At  the  magnetic  poles,  the 
inclination  is  90°;  at 
the  magnetic  equator, 
there  is  no  inclina- 
tion. The  inclination 
at  any  given  place  is 
not  greatly  different 
from  the  latitude  of 
that  place. 


(a.)  Experiments  for 
inclination  are  difficult 
of  execution  without  spe- 
cial apparatus.  It  is  diffi- 
cult to  make  a  needle 
turn  about  a  point  ex- 
actly coincident  with  its 
centre  of  gravity.  In 
rough  experiments,  there 
is  danger  that  the  mag- 
netic effect  will  be 


NORTH 
STAR 


fi* 


FIG.  223. 


MAGNETISM.  315 

Experiment  100. — Set  two  stakes  so  that  a  string  joining  them 
will  point  toward  the  North  Star.  The  string  will  run  north  and 
south  or  nearly  enough  so  for  our  purpose.  Place  a  long  magnet 
suspended  as  a  needle  under  or  over  the  string.  Looking  downward 
at  the  magnet  and  the  string,  it  will  probably  be  found  that  the 
needle  and  the  string  do  not  point  in  the  same  direction.  The 
North  Star  may  be  easily  found  any  evening  in  the  direction  indi- 
cated by  "The  Pointers"  of  the  well  known  constellation,  "The 
Great  Dipper."  "The  Pointers"  are  the  two  stars  marked  by  the 
Greek  letters  a  and  (3  in  Fig.  223. 

441.  Declination  or  Variation. — The  magnetic 
needle,  at  most  places,  does  not  lie  in  an  exact  north  and 
south  line.  The  angle  that  the  needle  makes  with 
the  geographical  meridian  is  its  declination  or 
variation.  A  line  drawn  through  all  places  where  the 
needle  points  to  the  true  north  is  called  a  Line  of  no  Vari- 
ation. Such  a  line,  nearly  straight,  passes  near  Cape  Hat- 
teras,  a  little  east  of  Cleveland,  Ohio,  through  Lake  Erie  and 
Lake  Huron.  It  is  now  slowly  moving  westward.  At  all 
places  east  of  the  Line  of  no  Variation,  the  —  end  of  the 
needle  points  west  of  the  true  north  ;  at  all  places  west  of 
the  Line  of  no  Variation,  the  variation  is  easterly.  The 
further  a  place  is  from  this  line,  the  greater  the  declina- 
tion, it  being  18°  in  Maine  and  more  than  20°  in  Oregon. 

(a.)  In  order  that  ships  may  steer  safely  by  the  compass,  magnetic 
charts  are  prepared.  The  declination  at  various  places  is  properly 
indicated  on  the  chart.  The  surveyor  must  recognize  not  only  the 
declination  of  his  needle  but  also  the  changes  in  declination.  Other- 
wise he  would  not  be  able  properly  to  "  run 
the  lines  "  of  a  given  piece  of  land  from  the 
description  given  in  an  old  deed. 


Experiment  101.  —  Construct  a  floating 
cell  of  zinc  and  copper  plates,  about  ^  inch 
apart,  the  connecting  wire  being  given  an  °  2  . 

elongated  spiral  or  solenoid  form,  and  support  ^TG.  224- 

it  by  a  large,  flat  cork  resting  on  the  surface  of  a  bowlful  of  acidu- 


316 


MAGNETISM. 


lated  water,  as  shown  in  Pig.  224.  The  solenoid  may  be  made  by 
winding  the  middle  part  of  about  3  yards  of  No.  20  insulated  copper 
wire  around  a  rod,  half  an  inch  in  diameter,  forming  thus  a  coil,  4 
or  5  inches  long.  The  current  will  set  the  axis  of  the  solenoid  in  a 
north  and  south  direction  as  if  it  were  a  magnetic  needle.  By  hold- 
ing one  end  of  a  bar  magnet  near  first  one  end  and  then  the  other 
end  of  the  solenoid,  it  will  be  found  that  the  latter  exhibits  magnetic 
polarity. 


FIG.  225.    ' 

Experiment  102. — Support  a  solenoid  by  placing  the  extremities 
of  its  wire  (bent  into  the  same  vertical  axis)  in  two  mercury  cups,  as 
shown  in  Fig.  225,  or  use  the  solenoid  of  the  floating  battery  above 
described.  Bring  the  end  of  a  second  solenoid  successively  to  the 
ends  of  the  first  and  notice  the  exhibition  of  magnetic  polarity. 

Experiment  103. — Send  a  current  of  electricity  from  the  small 
cell,  mentioned  in  Experiment  16,  through  its  wire.  Pour  half  a 
teaspoonful  of  iron  filings  upon  a  sheet  of  paper  and  bring  the  wire 
conductor  of  the  cell  into  contact  with  the  filings.  Notice  that  the 
filings  cling  to  the  wire  as  though  it  were  a  magnet.  Break  the 
circuit  and  notice  that  the  filings  fall  from  the  wire. 

442.  Electro -Magnets. — From  these  experiments, 
we  see  that  while  the  wire  conductor  is  carrying  an  electric 
current  it  has  the  properties  of  a  magnet.  We  have 
already  seen  that,  under  similar  circumstances,  the  con- 
ductor deflects  a  magnetic  needle  as  if  it  were  itself  a 


MAGNETISM. 


317 


FIG.  226. 


magnet.  In  fact,  such  a  conductor  is  a  temporary  mag- 
net. The  magnetic  effect  is  much  increased  if  a  con- 
siderable length  of  the  conductor  be 
made  of  insulated  wire  and  wound 
into  a  coil,  as  shown  in  Fig.  226. 
Such  a  coil  is  called  a  helix;  it  is  a 
magnet  with  a  +  pole  at  one  end  and 
a  --  pole  at  the  other.  It  has  an 
easily  perceptible  magnetic  field.  If 
a  soft  iron  rod  or  core  be  introduced 
into  the  coil,  it  enters  the  magnetic 
field  of  the  coil  or  helix  and  becomes 
a  magnet.  This  combination  of  coil  and  core  consti- 
tutes an  electro-magnet  and  is  more  powerfully  mag- 
netic than  the  coil  alone.  An  electro-magnet  is  a 
bar  of  iron  surrounded  ~by  a  coil  of  insulated  wire 
carrying  a  current  of  electricity.  It  may  be  made 
more  powerful  than  any  permanent  magnet  but  loses  its 
power  as  soon  as  the  current 
ceases  to  flow  through  its  coil. 
The  fact  that  the  magnetism  of 
this  apparatus  is  under  control 
adapts  it  to  many  important  uses, 
such  as  electric  bells  and  tele- 
graphic instruments. 


FIG.  227. 


443.  Forms  of  Electro- 
Magnets. — The  bar  of  §  416,  a, 
and  the  ring  of  Fig.  199,  with 
their  helices,  are  electro-magnets.  The  electro-magnet 
more  often  has  the  horse-shoe  form  shown  in  Fig.  227,  so 
that  the  attraction  of  both  poles  may  act  upon  the  same 


318  MAGNETISM. 

body  at  the  same  time.  The  middle  of  the  bent  bar  is 
bare,  the  direction  of  the  windings  on  the  ends  being  such 
that,  were  the  bar  straightened,  the  current  would  move 
in  the  same  direction  round  every  part.  More  frequently, 
the  two  helices,  A  and  B,  have  separate  cores  which  are 
joined  by  a  third  straight  piece  into  which  the  ends  of  the 
cores  are  screwed.  An  armature  is  often  placed  across  the 
two  poles  of  the  magnet,  as  shown  in  the  figure.  Electro- 
magnets have  been  made  capable  of  supporting  several 
tons. 

(a.)  When  the  circuit  is  broken  and  the  current  thus  interrupted, 
the  iron  is  generally  not  whotty  demagnetized.  The  small  magnet- 
ism remaining  is  called  residual  magnetism.  The  residual  magnetism 
seems  to  increase  with  the  hardness  and  impurity  of  the  iron.  The 
cores  of  electro-magnets  for  some  purposes  are  made  of  the  softest 
and  purest  iron  obtainable. 

444.  The  Electric  Telegraph.  —  The  electric 
telegraph  consists  essentially  of  an  electro-magnet  and  a 
"key"  placed  in  the  circuit  of  a  battery.  The  key  is  an 

instrument  by  which 
the  circuit  may  be 
easily  broken  or  closed 
at  will.  The  arm  at  u  re, 
A,  of  the  "register'' 
magnet,  M,  is  sup- 
ported by  a  spring,  8, 
which  lifts  it  when  the 
FlG  22g  circuit  is  broken. 

When    the    circuit   is 

closed,  the  armature  is  drawn  down  by  the  attraction  of 
the  magnet.  Thus,  the  armature  may  be  made  to  vibrate 
up  and  down  at  the  will  of  the  person  at  the  key.  The 


MA  GNETISM. 


319 


armature  may  act  upon  one  arm  of  a  lever,  the  other  end 
of  which,  being  provided  with  a  style  or  pencil,  P,  may  be 
pressed  against  a  paper  ribbon,  R,  drawn  along  by  clock- 
work. Thus,  the  pencil  may  be  made  to  record,  upon  the 
moving  paper,  a  series  of  dots  and  lines  at  the  pleasure  of 
the  operator  at  the  key  perhaps  hundreds  of  miles  away. 
When  the  two  stations  are  several  miles  apart,  one  of  the 
wires  is  dispensed  with,  the  circuit  being  completed  by 
connecting  each  station  with  the  earth.  This  arrange- 
ment saves  half  the  wire  and  nearly  half  the  cost  of  the 
line.  As  the  resistance  of  the  earth  is  insignificant,  there 
is  the  further  saving  of  nearly  half  the  battery  otherwise 
necessary.  Earth  connections  are  often  made  by  joining 
the  wires  to  water  or  gas  pipes  that  run  into  the  ground. 
When  the  line  is  long,  there  is  a  battery  at  each  end,  the 
+  electrode  of  one  battery  and  the  —  electrode  of  the 
other  battery  being  joined  to  the  line  wire.  The  same 
principle  of  communicating  signals  by  making  and  break- 
ing an  electric  circuit  is  used  in  fire  and  burglar  alarms, 
hotel  annunciators,  etc. 

445.  Morse's  Alphabet.  —  The  inventor  of  the 
practical  electric  telegraph  was  an  American,  S.  F.  B.  Morse. 
The  code  of  signals  devised  by  him  is  given  below : 


I 

ETTERS. 

a    — 

k 



b  

I 



c  -  -    - 

m 



d  

n 



e  - 

0 

.      - 

71 

'.  "'  £ 

P 

g  

q 



h  

j      —       .       -_       . 

r 

8 

t 

:.:•  g 

u 


z  - 


320 


MAGNETISM. 


(a.)  To  prevent  confusion,  a  small  space  is  left  between  successiva 
letters,  a  longer  one  between  words  and  a  still  longer  one  between 
sentences.  We  here  give  a  short  message  written  in  Roman  and  in 
telegraphic  characters : 


H 


1      1 


ten 


The  ordinary  telegraph  operator  does  not  punctuate  his  messages 
to  any  considerable  extent.     Telegraph  operators  soon  become  so 


FIG.  229. 

familiar  with  this  alphabet  that  they  understand  a  message  from  the 
mere  clicks  of  the  lever  and  do  not  use  any  recording  apparatus. 
Such  an  operator  is  said  to  "  read  by  sound";  his  instrument  is  called 
a  "sounder."  Fig.  229  represents  one.  The  sounder  is  placed  on  a 
local  circuit  and  has  a  usual  resistance  of  from  three  to  five  ohms. 


FIG.  230. 

(6.)  With  a  long  main  line,  the  resistance  is  so  great  that  the  cur- 
rent of  the  inain  battery  is  too  feeble  to  operate  the  sounders  with 


MAGNETISM. 


321 


sufficient  force.  This  difficulty  is  met  |4| 
by  introducing  a  "  local  battery  "  and 
a  "  relay  "  at  each  station  on  the  line. 
The  relay  (Fig.  230)  is  a  delicate  elec- 
tro-magnet, of  which  the  terminals, 
a  and  6,  are  connected  with  the  main 
line.  This  magnet  operates  an  ar- 
mature lever,  e,  the  end  of  which 
strikes  against  a  metal  contact  piece 
and  thus  closes  the  local  circuit 
through  the  terminals,  c  and  d.  The 
resistance  of  relays  vary  from  50  to 
500  ohms.  The  "  Western  Union  " 
standard  relay  has  a  resistance  of  150 
ohms. 

(c.)  The  arrangement  of  instru- 
ments is  best  studied  at  a  telegraph 
station,  one  or  more  of  which  may  be 
found  at  almost  any  town  or  railway 
station.  The  general  features  of  the 
"  plant "  are  represented  by  the  dia- 
gram shown  in  Fig.  231.  The  pupil 
will  probably  find  the  key,  sounder 
and  relay  on  a  table  and  the  local 
battery,  6,  under  the  table.  The  keys 
being  habitually  closed,  the  current 
passes  through  all  relays  on  the  line, 
the  current  being  continuous  (§  395) 
except  when  a  message  is  being  sent 
from  some  office.  When  an  operator, 
in  sending  a  message,  opens  his  key, 
the  breaking  of  the  circuit  stops  the 
current,  demagnetizes  the  relays  and 
allows  their  springs  to  draw  back  the 
armature  levers,  e.  This  breaks  each 
local  circuit  and  demagnetizes  each 
sounder,  the  spring  of  which  raises 
its  armature.  Things  are  now  as 
shown  in  the  diagram,  which  also 
represents  the  condition  of  affairs  at 
every  other  station  on  the  line.  When 
a  message  is  sent  from  any  station, 
each  relay  lever,  e,  acts  as  a  key  to 


FIG.  231. 


TL. 

its  local  circuit,  it  and  the 


322  MAGNETISM. 

sounder  lever  vibrating  in  obedience  to  the  motions  of  the  key  at 
the  sending  station.  Of  course,  the  sending  operator  can  read  his 
own  message  from  his  sounder.  The  message  may  also  be  read  from 
any  sounder  on  the  line. 

(d.)  If  the  local  circuit  at  New  York  (see  Fig.  231)  be  lengthened 
so  as  to  reach  thence  to  Boston  and  the  local  battery,  b,  be  increased 
to  the  dimensions  of  a  main  battery,  B,  (ground  connections  being 
made,  of  course),  the  relay  at  New  York  will  transmit  to  Boston  the 
message  received  from  Cleveland.  In  such  cases,  the  relay  at  New 
York  becomes  a  repeater.  Messages  from  New  York  to  Chicago  may 
thus  be  repeated  at  Meadville,  Pa.,  without  the  intervention  of  any 
operator. 

446.  Duplex  and  Quadruplex  Telegraphy.— 

The  simple  Morse  system,  just  described,  is  very  reliable, 
but  a  given  wire  can  transmit  only  one  message  at  a  time. 
By  what  is  known  as  the  duplex  system,  a  wire  may  be 
made  to  convey  two  messages,  one  each  way,  at  the  same 
time,  without  conflict.  By  what  is  known  as  the  quadru- 
plex  system,  a  wire  may  be  made  to  carry  four  messages, 
two  each  way,  at  the  same  time.  Delany's  multiplex  sys- 
tem enables  the  sending  of  six  messages  in  the  same  direc- 
tion at  one  time.  The  student  is  referred  to  technical 
works  on  telegraphy  for  an  explanation  of  these  systems. 
A  good  Morse  operator  can  send  or  receive  thirty  or  forty 
words  a  minute ;  by  the  aid  of  a  combination  of  recent 
inventions,  fifteen  hundred  words  have  been  transmitted 
over  a  single  wire  in  one  minute. 

447.  Electric    Bells. — The    construction    of    the 
trembler  or  electric  bell  will  be  clearly  seen  by  an  exam- 
ination of  Fig.  232.     When  the  button  at  P  (anywhere 
on  the  circuit)  is  pushed,  two  metal  pieces  are  brought 
into  contact  and  the  circuit  is  thus  completed.     The  spring 
carried  by  the  armature  of  the  magnet,  E,  makes  contact 


MAGNETISM. 


323 


with  the  tip  of  the  screw  at   (7,  except  when  it  is  drawn 
away  by  the  attraction  of  the  magnet. 


FIG.  232. 

(a.)  When  the  spring  rests  against  the  end  of  the  screw  at  C  (the 
circuit  being  closed  at  P),  the  cores  of  E  are  magnetized.  They 
then  draw  the  armature  away  from  the  end  of  the  screw  and  break 
the  circuit  at  C.  E,  being  thus  demagnetized,  no  longer  attracts  its 
armature,  which  is  thrown  back  against  the  end  of  the  screw  by  the 
elasticity  of  the  spring  that  supports  it.  It  is  then  again  attracted 
and  released,  thus  vibrating  rapidly  and  striking  a  blow  upon  the 
bell  at  H  at  every  vibration.  (See  §  459,  a.) 


324  MAGNETISM. 

448.  Making  Permanent  Magnets. — A  com- 
mon way  of  magnetizing  a  steel  bar  is  to  draw  one 
end  of  a  strong  magnet  from  one  end  of  the  bar 
to  the  other,  repeating  the  operation  several  times, 
always  in  the  same  direction.  A  second  method  is  to 
bring  together  the  opposite  poles  of  two  magnets  at  the 
middle  of  the  bar  to  be  magnetized  and  simultaneously 
drawing  them  in  opposite  directions  from  the  middle  to 
the  ends.  A  steel  bar  may  be  magnetized  by  striking  it 
on  end  with  a  wooden  mallet  while  it  is  held  in  the  direc- 
tion assumed  by  the  dipping  needle.  If  a  bar  of  steel  be 
heated  to  redness  and  cooled,  either  slowly  or  suddenly, 
while  lying  in  the  magnetic  meridian,  it  acquires  magnetic 
polarity.  But  better  than  any  of  these  can  give  are  the 
effects  produced  by  electro-magnetism. 


FIG.  233. 

The  bar  may  be  permanently  magnetized  by  drawing  it, 
from  its  centre,  in  one  direction  over  one  pole  of  a  power- 
ful electro-magnet  and  then,  from  its  centre,  in  the  oppo- 
site direction  over  the  other  pole  and  repeating  the  pro- 
cess a  few  times  (Fig.  233). 

A  bar  of  steel  placed  within  a  helix  through  which  a 


MAGNETISM. 


325 


strong  current  is  passing  will  be  permanently  magnetized. 
The  bar  should  be  passed  into  one  end  of  the  helix  and 
removed  from  the  other  end. 

(a.)  A  long,  thin,  steel  magnet  is  more  powerful  in  proportion  to 
its  weight  than  a  thicker  one  is.  Compound  magnets  are,  therefore, 
made  of  thin  pieces  of  steel,  separately  magnetized  and  then  bound 
together  in  bundles.  A  horse-shoe  magnet  will  lift  a  load  three  or 
four  times  as  heavy  as  will  a  bar  magnet  of  the  same  weight.  The 
lifting  power  is  increased  if  the  area  of  contact  between  the  poles  and 
the  armature  is  increased.  The  lifting  power  of  a  magnet  is  strength- 
ened, in  an  unexplained  way,  by  gradually  increasing  the  load  on  its 
armature  day  by  day  until  it  bears  a  load  which  at  the  outset  it 
could  not  have  borne.  If  the  load  be  so  increased  that  the  armature 
is  torn  off,  the  power  of  the  magnet  falls  at  once  to  its  original 
value.  The  attraction  between  a  powerful  electro-magnet  and  its 
armature  may  amount  to  200  Ib.  per  square  inch,  or  14,000  g.  per 
sq.  cm.  Small  magnets  lift  a  greater  load  in  proportion  to  their  own 
weight  than  large  ones.  A  good  steel  horse-shoe  magnet  weighing 
one  pound  ought  to  lift  twenty  pounds'  weight. 
A  steel  magnet  loses  part  of  its  magnetism  by  be- 
ing jarred  or  knocked  about  and  all  of  it  by  being 
heated  to  redness. 


449.  Armatures. — Magnets  left  to  them- 
selves soon  lose  their  magnetism.  They  should, 
therefore,  be  provided  with  armatures.  Armatures 
are  pieces  of  soft  iron  placed  in  contact  with  opposite 
poles,  as  shown  in  Fig.  234.  The  two  pojes  of  the 
magnet  (or  magnets,  for  two  bar  magnets  may  be 
thus  protected)  act  inductively  upon  the  armature 
and  produce  in  it  poles  opposite  in  kind  to  those 
with  which  they  come  in  contact.  The  poles  of  the 
armature  in  turn  react  upon  the  magnet  and,  by 
their  power  of  attraction,  aid  in  retaining  the  mag- 
netism. 


FIG.  234. 


45O.  Magnetic  Units, — All  magnetic  quantities,  strength  of 
poles,  intensity  of  magnetization,  etc.,  are  expressed  in  terms  of 
special  units  derived  from  the  fundamental  units  of  length,  mass  and 
time,  i.e.,  they  are  0.  G.  S.  units. 

(a.)  Unit  Strength  of  Magnetic  Pole. — The  unit  magnetic  pole  is 


326  MAGNETISM. 

one  of  such  strength  that  it  repels  a  similar  pole  of  equal  strength 
with  a  force  of  one  dyne  when  it  is  placed  at  a  distance  of  one  centi- 
meter from  it. 

(&.)  Magnetic  Potential  being  measured  by  work  done  in  moving 
a  unit  magnetic  pole  against  the  magnetic  forces,  the  unit  of  mag- 
netic potential  will  be  measured  by  the  unit  of  work,  the  erg. 

(c.)  Unit  Difference  of  Magnetic  Potential  exists  between  two 
points  when  it  requires  the  expenditure  of  one  erg  of  work  to 
bring  a  —  unit  magnetic  pole  from  one  point  to  the  other  against 
the  magnetic  forces. 

(d.)  Intensity  of  Magnetic  Field  is  measured  by  the  force  it  exerts 
upon  a  unit  magnetic  pole ;  hence, 

(e.)  Unit  Intensity  of  Field  is  that  which  acts  on  a  unit  —  pole 
with  a  force  of  one  dyne. 

451.  Electro-Magnetic  Units.— The  magnetic  units  just 
described  give  rise  to  a  set  of  electrical  units,  in  which  the  strength 
of  currents,  etc.,  are  expressed  in  magnetic  measures.  (See  §  320.) 

(a.)  Unit  Strength  of  Current. — A  current  has  unit  strength  when 
1  cm.  length  of  its  circuit  bent  into  an  arc  of  1  cm.  radius  (so  as  to 
be  always  1  cm.  away  from  the  magnet-pole)  exerts  a  force  of  one 
dyne  on  a  unit  magnet-pole  placed  at  the  centre. 

(b.)  Unit  of  Quantity  of  Electricity  is  that  quantity  which  is  con- 
veyed by  unit  current  in  one  second. 

(c.)  Unit  of  Difference  of  Potential  (or  of  E.  M.  F.)  is  that  which 
exists  between  two  points  when  it  requires  the  expenditure  of  one 
erg  of  work  to  bring  a  unit  of  +  electricity  from  one  point  to  the 
other  against  the  electric  force. 

(d.)  Unit  of  Resistance. — A  conductor  possesses  unit  resistance 
when  unit  difference  of  potential  between  its  ends  causes  a  current 
of  unit  strength  to  flow  through  it. 


452.  Practical  Units.— As  some  of  these  "abso- 
lute" electro-magnetic  units  are  too  large  for  common, 
convenient  use  and  others  are  too  small,  the  practical 
units,  the  volt,  the  ohm,  the  ampere,  the  coulomb  and 
the  farad  have  been  chosen  and  are  generally  used.  These 
units  have  been  already  described,  the  value  of  each  in 
absolute  electro-magnetic  units  being  given. 


MAGNETISM.  327 

453.  Molecular    Changes   in   a   Magnet. — 

When  a  steel  or  iron  bar  is  strongly  magnetized,  it  in- 
creases in  length  and  diminishes  in  thickness.  This  effect 
is  probably  due  to  the  magnetization  of  the  individual  mole- 
cules, which  tend  to  set  themselves  parallel  to  the  length 
of  the  bar.  This  supposition  is  confirmed  by  the  observa- 
tion that  at  the  moment  when  a  bar  is  magnetized  or 
demagnetized,  a  faint  metallic  click  is  heard  in  the  bar. 
When  a  tube  containing  water  rendered  muddy  with  finely 
divided  magnetic  oxide  of  iron  is  magnetized,  the  liquid 
becomes  clearer  in  the  direction  of  magnetization,  the  par- 
ticles apparently  setting  themselves  end  to  end  and  al- 
lowing more  light  to  pass  between  them.  A  piece  of  iron, 
when  powerfully  magnetized  and  demagnetized  in  rapid 
succession,  grows  hot,  as  if  the  changes  were  accompanied 
by  internal  friction. 

454.  Theory  of  Magnetism. — These  and  other 
phenomena  point  to  a  theory  of  magnetism  very  different 
from  the  old  notion  of  "  magnetic  fluids."    It  appears  that 
every  molecule  of  a  magnet  is  itself  a  magnet  and  that  the 
molar  magnet  becomes  a  magnet  only  by  the  molecular 
magnets  being  turned  so  as  to  point  one  way.     This  con- 
clusion is  supported  by  the  observation  that  if  a  glass  tube 
full  of  iron  filings  be  magnetized,  the  filings  may  be  seen 
to  set  themselves  endwise  and  that,  when  thus  once  set, 
they  act  as  a  magnet  until  they  are  shaken  up. 

455.  Relation  of  Magnetism  to  Energy. — A 

magnet  is  a  reservoir  of  potential  energy.  This  energy  is 
due  to  tHe  expenditure,  at  some  time,  of  a  definite  amount 
of  energy,  of  some  kind.  By  virtue  of  its  potential  energy, 


328  MAGNETISM. 

it  can  do  a  definite  amount  of  work  and  no  more.  For  in- 
stance, it  may  attract  a  certain  amount  of  iron.  When 
thus  fully  loaded,  the  magnet  has  done  its  full  work  and 
can  do  no  more.  When  the  iron  is  torn  from  the 
magnet,  more  energy  is  expended  and  the  magnet 
thus  endowed  again  with  potential  energy.  A 
magnet  has  not  an  inexhaustible  supply  of  energy, 
as  some  have  supposed. 

EXERCISES. 

1.  (a.)    What  is  a  magnetic   pole?     (6.)    A  magnetic  equator? 
(c.)  How  does  a  magnet  behave  toward  soft  iron?    (d.)  How  does 
soft  iron  behave  toward  a  magnet  ? 

2.  (a.)  State  carefully  the  various  effects  that  one  magnet  may 
exert  upon  a  second  magnet.     (&.)  Generalize  these  observed  facts 
into  a  law. 

3.  On  board  an  iron  ship  that  is  laying  a  submarine  telegraph 
cable,  there  is  a  galvanometer  used  for  testing  the  continuity  of  the 
cable.     It  is  necessary  to  prevent  the  magnetized  needle  of  the  gal- 
vanometer from  being  affected  by  the  magnetism  of  the  ship.    How 
can  this  be  done  ? 

4  (a.)  Given  a  bar  magnet,  how  would  you  determine  the  sign  of 
either  of  its  poles?    (6.)  What  is  a  diamagnetic  substance  ? 

5.  If  a  magnetic  needle  be  freely  suspended  from  its  centre  of 
gravity,  what  position  will  it  assume? 

6.  (a.)  Do  you  think  that  the  earth  is  a  magnet?    (&.)  Give  a  good 
reason  for  your  answer,      (c.)  Do  the  magnetic  and  the  geographical 
meridians  ever  coincide?     (d.)   Do  they  always  coincide?     (e.)  If 
they  do  not  coincide,  what  name  would  you  give  to  their  difference 
in  direction  ? 

7.  (a.)  Does  the  magnetic  attraction  of  the  earth  upon  a  ship's 
compass  tend  to  float  the  ship  northward  ?    (&.)  If  so,  why?    If  not, 
why  not  ? 

8.  (a.)  State  and  illustrate  the  second  law  of  motion.     (6.)  State 
and  illustrate  the  law  of  universal  gravitation,     (e.)  A  body  falls  to 
the  ground  from  rest  in   11  seconds ;  what  is  the  space  passed  over? 

9.  An  electric  bell  in  Cleveland,  Ohio,  is  to  be  rung  by  a  battery 
in  New  York  City.     Should  the  magnet  coils  of  the  bell  be  made  of 
fine  or  coarse  wire  ? 


MAGNETISM. 


329 


10.  Would  you  use  a  long  coil  or  a  short  coil  galvanometer  to 
measure  the  current  used  to  ring  the  bell  above  mentioned? 

11.  Would  it  make  any  difference  whether  the  galvanometer  were 
put  into  the  circuit  at  New  York  or  at  Cleveland  if  the  line  be  thor- 
oughly insulated  ? 

12.  With  a  local  battery  of  2  cells,  each  having  an  internal  resist- 
ance of  2  ohms,  what  should  be  the  resistance  of  the  sounder  ? 

13.  The  cells  represented  in  Fig.  235  have  each  an  E.  M.  F.  of  2 
volts  and  an  internal  resistance  of  3  ohms. 

What  is  the  resistance  of  the  external  cir- 
cuit, G,  if  the  battery  is  arranged  in  the  best 
possible  way  ?  Ans.  2  ohms. 

14.  Why  is  it  that  when  there  is  little  other 
resistance  in  the  circuit,  a  stout  wire  with  few 
turns  will  make  a  stronger  electro-magnet  than 
a  very  fine  wire  with  many  more  turns? 

15.  A  battery  of  5  Leclanche  cells  was  con- 
nected in  simple  circuit  with  a  galvanometer 
and  a  box  of  resistance  coils.     A  deflection  of 
40°  having  been  obtained  by  adjustment  of  the 
resistances,  it  was  found  that  the  introduction 
of  150  additional  ohms  of  resistance  brought 
down  the  deflection  to  29°.     A  battery  of  ten 
Daniell's  cells  was  then  substituted  in  the  cir- 
cuit and  adjusted  until  the  resistance  was  40° 
as  before.     But  this  time  it  was  found  that  216 

ohms  had  to  be  added  before  the  deflection  was  brought  down  to 
29°.  Taking  the  E.  M.  F.  of  a  single  Daniell's  cell  as  1.079  volt, 
calculate  that  of  a  single  Leclanche  cell.  Ans.  1.499  volt. 

16.  An  electric  bell  has  a  resistance  of  0.5  ohm.    It  requires  a 
current  of  20  milliamperes  to  ring  it.     It  is  on  a  line  of  1  mile 
of  No.  20  copper  wire  (see  Appendix  I).     Ignoring  the  internal  re- 
sistance of  the  battery,  find  how  many  Leclanche  cells  (E.  M.  F. 
=  1.6  volts)  will  be  required. 

17.  We  have  to  send  a  current  through  a  telegraph  line,  100  miles 
long,  the  resistance  of  which  is  13  ohms  per  mile.     The  battery  is 
composed  of  Daniell  cells,  each  having  an  E.  M.  F.  of  1.079  volts  and 
an  internal  resistance  of  2  ohms.     The  telegraphic  instrument  offers 
a  resistance  of  130  ohms  and  requires  a  current  of  10  milliamperes 
to  work  it.     Will  one  cell  of  battery  answer  our  purpose?    Why  ? 

18.  Under  what  circumstances  will  a  magnet  repel  an  unmag- 
netized  piece  of  iron  ? 


FIG.  235. 


330  MAGNETISM. 

19.  Give  two  or  three  differences  between  electric  attractions  and 
repulsions  and  magnetic  attractions  and  repulsions. 

20.  A  zinc  and  a  copper  plate  are  respectively  united  by  copper 
wires  to  the  terminals  of  a  galvanometer.     They  are  dipped,  side  by 
side,  into  a  glass  containing    dilute   sulphuric   acid.      The  galva- 
nometer needle,  at  first,  shows  a  deflection  of  28°,  but  five  minutes 
later  the  deflection  has  fallen  to  11°.    How  do  you  account  for  this 
falling  off  ? 

21.  A  wire,  the  resistance  of  which  was  to  be  determined,  was 
placed  in  a  Wheatstone's  bridge,  in  which  resistances  of  10  and  100 
ohms  respectively  were  used  as  the  fixed  resistances.     Its  resistance 
was  balanced  when  the  adjustable  coils  were  arranged  to  throw  281 
ohms  into  circuit.     What  was  its  resistance  ?    (See  Appendix  M,  (>.].) 

Ana.  28.1  ohms. 

22.  Relays  are  wound  with  long,  fine  wire  and  sounders  with 
short,  stout  wire.     Why  is  there  this  difference  ? 


MAGNETISM.  331 

Recapitulation.— To  be  amplified  by  the  pupil  for 


review. 


f  MAGNETS. 


OQ 

*— i 

w 

125 


NATUKAL. 
(  Forms. 

PERMANENT  •< 
(  How  Made. 

Definition. 

ARTIFICIAL.  .  .  - 

Advantages. 

TEMPORARY  OR 

Forms. 

ELECTRO-MAGNETS. 

Residual 

Magnetism. 

Telegraph. 

Electric  Bells. 

{MAGNETS. 

CHANGES. 

POLES. 

CHARACTERISTICS. 

LAWS. 

(  MAGNETIC               .  ) 

(.RELATION  TO-J                                     \Substances. 

DlAMAGNETIC. 


RETENTIVITY. 


THEORY. 

fBY  CONTACT. 

MAGNETIZATION.  \  MODES  OF. 

I  BY   INDUCTION.  -I 


.MAGNETIC  FIELD. 
LINES  OF  FORCE. 
PRECEDES  ATTRACTION. 
MAGNETIC  SCREENS. 


TERRESTRIAL.. 


POLES.  f  COMPASS. 

MAGNETIC  NEEDLES.  \  DIPPING. 
DIP.  [  ASTATIC. 

DECLINATION. 


MAGNETIC   AND   ELECTRO-MAGNETIC   UNITS. 
RELATION  TO  ENERGY, 


-3 


ECTFON   V. 


INDUCED     E  LECTRI  CITY. 

456.  Induced    Currents.  —  From  our  study  of 
frictional  electricity  and  magnetism,  we  are  familiar  with 
the  term  induction,  by  which  we  understand  the  influence 
that  an  electrified  body  exerts  upon  a  neighboring  un elec- 
trified body  or  that  a  magnetized  body  exerts  upon   a 
neighboring  magnetic  but  unmagnetized  body.     In  1831, 
Faraday  discovered  an  analogous   class    of    phenomena 
which  we  are  now  about  to  consider.     An  induced,  cur- 
rent is  a  current  produced   in  a  conductor  by  the 
influence  of  a  neighboring  current  or  magnet.     A 
current  used  to  produce  such  an  effect  is  called  an  in- 
ducing current. 

457.  Inductive  Effect  of  Closing  or  Break- 
ing  a   Circuit. — In  Fig.  236,  B  represents  a  double 
coil  made  as  follows:     On  a  hollow  cylinder  of  wood  or 
card-board  are  wound  several  layers  of  stout,  insulated, 
copper  wire.    The  two  ends  of  this  wire,  which  constitutes 
the  primary  coil,  are  seen  dipping  into  the  cups,  gg'.   Upon 
this  coil  and  carefully  insulated  from  it,  is  wound  a  much 
greater  length  of  finer,  insulated  copper  wire.    The  two  ends 
of  this  wire,  which  constitutes  the  secondary  coil,  are  seen 
connecting  with  a  delicate,  long  coil  galvanometer,   G. 


INDUCED  ELECTRICITY. 


333 


Remember  that  there  is  no  electrical  connection  between 
the  two  coils.  Wires  from,  the  poles  of  a  voltaic  cell,  P, 
dip  into  mercury  in  the  cups  g  g',  thus  closing  a  circuit 
through  the  primary  coil  of  B.  While  this  circuit  is  closed, 
the  galvanometer  needle  is  at  rest,  showing  that  no 
current  is  passing  through  the  secondary  coil.  By  lifting- 
one  of  the  wires  from  its  cup,  the  inducing  current  is 
interrupted.  At  this  instant,  the  galvanometer  needle 


FIG.  236. 

is  deflected,  as  by  a  sudden  impulse  that  immediately 
passes  away.  This  movement  of  the  galvanometer  needle 
shows  the  existence  of  a  momentary,  induced  current  in 
the  secondary  coil.  The  direction  in  which  the  needle 
turns,  shows  that  the  secondary  current  is  direct,  i.  e., 
that  it  has  the  same  direction  as  the  inducing  cur- 
rent. If  the  wire  just  removed  from  the  cup  be  replaced 
and  the  inducing  current  thus  re-established,  the  galva- 
nometer needle  will  be  momentarily  turned  in  the  direction 
opposite  to  that  in  which  it  was  previously  turned.  When 
a  current  begins  to  flow  through  the  primary  coil, 
it  induces  a  current  in  the  secondary  coil.  When 


334  INDUCED  ELECTRICITY. 

it  ceases  to  flow  through  the  primary  coil,  a  cur- 
rent flowing  in  the  opposite  direction  is  induced 
in  the  secondary  coil.  Both  induced  currents  are 
merely  momentary  in  duration. 

458.  The   Extra   Current.— When  a  circuit  is 
made  or  broken,  each  convolution  of  a  coil  placed  in  £he 
circuit  acts  inductively  upon  the  other  convolutions  of 
the  coil  as  if  they  were  portions  of  two  unconnected  cir- 
cuits.     This   action    is    called    the   induction   of  a 
current  upon  itself ;    the  current  thus  produced  is 
vailed  the  extra  current. 

(a.)  When  the  circuit  is  made,  the  extra  current  is  inverse  or 
opposite  in  direction  to  the  primary  current  and  acts  against  it. 
The  extra  current  at  the  breaking  of  the  circuit  is  direct  and  adds 
its  effect  to  that  of  the  primary  current.  Hence,  a  spark  is  more 
often  seen  on  breaking  than  on  making  contact.  Increasing  the 
number  of  coils  or  convolutions  in  the  circuit  will  increase  the  brill- 
i-mcy  of  the  spark.  If  the  coil  has  an  iron  core  (electro-magnet) 
the  effect  is  especially  marked. 

459.  Ruhmkorff's    Coil.  —  The  induction  coil, 
often  called,  from  the  name  of  its  inventor,  Ruhmkorff's 
coil,  is  a  contrivance  for  producing   induced,   cur- 
rents in  a  secondary  coil  by  closing   and   opening, 
in   rapid   succession,  the   circuit  of  a    current   in 
the  primary  coil.     The  essential  parts  are  described  in 
§  457.     In  the  complete  instrument,  the  axis  of  the  coils 
is  a  bundle  of  soft  iron  wires.     These  wires  usually  ter- 
minate in  two  small  plates  of  soft  iron  which  thus  form 
the  ends  of  the  wire  bundle.    Around  this  bundle,  is  wound 
the  primary  coil  of  stout,  insulated,  copper  wire.     Upon 
the  primary  coil,  but  carefully  insulated  from  it,  is  wound 


INDUCED   ELECTRICITY. 


335 


the  secondary  coil  which  is  made  of  a  great  many  turns  of 
fine,  silk  covered,  copper  wire. 

(a.)  The  wire  bundle  (M,  Fig.  238)  becomes  magnetized  by  the 
action  of  the  battery  current  in  the  primary  coil  and  then  adds  its 
Inductive  effect 
upon  the  secondary 
coil  to  the  effect  of 
tKe  primary  itself. 
The  primary  cir- 
cuit is  rapidly 
broken  and  closed 
by  an  automatic  in- 
terrupter or  contact 
breaker,  repre- 
sented at  the  left 
hand  of  the  coil, 
Fig.  237,  and  at  the  FIG.  237. 

right  hand  of  the 

diagram  in  Fig.  238.  One  of  the  posts  there  seen  carries  an  elastic, 
metallic,  vibrating  plate  with  an  iron  hammer,  b,  at  its  end.  This 
hammer  vibrates  back  and  forth  between  the  end  of  the  iron  core  of 
the  coils  and  the  end  of  the  metal  adjusting  screw,  d,  which  is  car- 
ried by  the  other  post  seen  in  the  figure.  These  posts  are  in  the 

primary  circuit.  When 
the  hammer  rests  against 
the  end  of  the  adjusting 
screw,  the  circuit  is  closed 
and  the  iron  core  is  mag- 
netized. As  soon  as  the 

*\  j^  core  is  magnetized,  it  at- 

tracts the  hammer,  thus 
drawing  it  away  from  the 
end  of  the  screw  and  break- 
ing the  circuit.  As  soon  as  the  circuit  is  broken,  the  bar  is  de- 
magnetized and  the  plate,  by  virtue  of  its  elasticity,  throws  the 
hammer  back  against  the  screw,  closing  the  circuit  and  again  mag- 
netizing the  core.  The  plate  is  thus  made  to  vibrate  with  great 
rapidity,  each  oscillation  making  or  breaking  the  primary  circuit  and 
creating  a  series  of  induced  currents  in  the  secondary  coil. 

(6.)  The  condenser  (C  G,  Fig.  238),  which  is  generally  placed  in 
the  pedestal  or  base  of  the  coil,  consists  of  a  number  of  sheets  of 
tinfoil  insulated  from  each  other  by  thin  sheets  of  varnished  paper 


336  INDUCED  ELECTRICITY. 

or  oiled  silk.  Alternate  layers  of  the  tinfoil  are  connected,  i.  e.,  the 
first,  third,  fifth,  seventh,  etc.,  layers  are  connected,  as  also  are  the 
second,  fourth,  sixth,  eighth,  etc.,  thus  forming  two  separate,  in- 
sulated series.  One  series  (e.  g.,  the  odd  numbered  sheets)  is  con- 
nected with  one  of  the  posts  of  the  contact  breaker  ;  the  other  series, 
with  the  other  post.  Thus,  the  plates  of  the  condenser  do  not 
form  a  part  of  the  primary  circuit  but  are,  as  it  were,  lateral  expan- 
sions of  that  circuit,  one  on  each  side  of  the  contact  breaker.  The 
effect  of  the  condenser  is  to  lessen  the  spark  when  the  primary  cir- 
cuit is  made  or  broken  and  to  increase  the  force  of  the  discharge  of 
the  secondary  coil. 

(c.)  For  an  ordinary  Ruhmkorff's  coil,  one  to  three  Bunsen  or 
potassim  di-chromate  elements  will  suffice. 

(d.)  Most  induction  coils  are  provided  with  a  commutator,  for  the 
purpose  of  changing  the  direction  of  the  current  through  the  primary 
coil  and,  consequently,  the  direction  of  the  currents  induced  in  the 
secondary  coil.  One  form  of  the  commutator  is  shown  at  the  right 
hand  end  of  Fig.  237.  It  is  not  an  essential  part  of  the  instrument. 

Experiment  104. — Let  the  members  of  the  class  join  bare  hands. 
Let  the  pupil  at  one  end  of  the  line  place  a  finger  on  one  of  the 
binding  posts  or  electrodes  of  the  secondary  coil  of  a  small  induction 
coil.  Then  let  the  pupil  at  the  other  end  of  the  line,  momentarily 
touch  the  other  electrode.  Each  person  in  the  line  will  feel  a 
"shock."  The  experiment  should  not  be  tried  with  a  powerful  coil, 
as  the  spasmodic,  muscular  contractions  thus  produced  are  sometimes 
painful  and  permanently  injurious. 

46O.  Spark  from  the  Induction  Coil.— If  the 

ends  of  the  secondary  coil  be  connected,  opposite  current* 
alternately  traverse  the  connecting  wire.  When  the  ends 
are  disconnected,  the  inverse  current  cannot  overcome  the 
resistance  of  the  intervening  air  because  of  its  low  electro- 
motive power  (§  458,  a).  The  direct  current,  produced 
by  breaking  the  primary  circuit,  is  alone  able  to 
force  its  way  in  the  form  of  a  spark.  The  sparks 
vary  with  the  power  of  the  instrument. 

(a.)  Mr.  Spottiswoode,  of  London,  has  made  an  induction  coil,  the 
secondary  coil  of  which  contains  280  miles  of  wire  wound  in  340,000 
turns.  This  magnificent  instrument  has  a  resistance  of  more  than 


INDUCED  ELECTRICITY. 


337 


100,000  ohms,  and,  when  worked  with  a  battery  of  30  Grove  cells, 
yields  a  spark  42|  inches  long, — a  result  greater  than  that  obtainable 
from  any  electric  machine.  The  induction  coil  may  be  used  to  pro- 
duce any  of  the  effects  of  frictional  electricity,  it  being  at  the  same 
time  nearly  free  from  the  limitations  that  atmospheric  moisture 
places  upon  ordinary  electric  machines. 

(6.)  For  many  instructive  and  beautiful  experiments  with  this  in- 
strument and  other  information  relating  thereto,  see  the  little  book, 
"  Induction  coils : — How  made  and  how  used,"  published  by  D.  Van 
Nostrand,  New  York ;  Price,  50  cents. 

461.  Currents  Induced  by  Change  of  Dis- 
tance.— If  the  primary  coil  be  made  movable,  as  shown 
in  Fig.  239,  and,  with  a  current  passing  through  it,  be 
suddenly  placed  within  the  sec- 
ondary coil,  the  galvanometer 
will  show  that  an  inverse  current 
is  induced  in  the  outer  coil. 
When  the  needle  has  come  to 
rest,  let  the  primary  coil  be  re- 
moved and  the  galvanometer 
will  show  that  a  direct  current 
is  induced.  From  this  we  see 
that  when  the  primary  coil, 
bearing  a  current,  is  brought 
near  or  thrust  into  the  sec- 
ondary coil,  an  inverse  cur- 
rent is  induced  in  the  latter ; 
that  when  the  coils  are  sep- 
arated, a  direct  current  is 

induced  in  the  secondary  coil;  that  the  induced 
currents  flow  while  a  change  of  distance  is  varying 
the  inductive  effect  of  the  primary  current.  Re- 
moving the  primary  coil  to  an  infinite  distance  is  equiva- 
lent to  breaking  its  circuit,  as  in  §  457. 


FIG.  239. 


338 


INDUCED    ELECTRICITY. 


462.  Magneto -Electric  Currents. —  We  have 
already  noticed  that  there  is  an  intimate  relation  between 
electric  and  magnetic  action.  We  have  seen  that  an  elec- 
tric current  may  develop  magnetism.  Faraday  found  that 
electricity  may  he  developed  by  magnets ;  the  results  of  this 
discovery  have  already  become  of  incalculable  commercial 
importance.  If,  instead  of  the  primary  coil  bearing  the 


FIG.  240. 

inducing  current,  a  bar  magnet  be  used,  as  shown  in  Fig. 
240,  the  effects  produced  will  be  like  those  stated  in  the 
last  paragraph.  WTien  the  magnet  is  thrust  into  the 
interior  of  the  coil,  an  induced  current  will  flow 
while  the  motion  of  the  magnet  continues.  When 
the  magnet  becomes  stationary,  the  current  ceases  to 
flow  and  the  needle  of  the  galvanometer  gradually 
comes  to  rest.  When  the  magnet  is  withdrawn,  an 
induced  current  flows  in  the  opposite  direction. 
Of  course,  it  makes  no  difference  whether  the  magnet  be 


TNDVCED   ELECTRICITY. 


339 


moved  toward  the  coil  or  the  coil  be  moved  toward  the 
magnet.  The  more  rapid  the  motion,  the  greater  will  be 
the  electromotive  force  of  the  induced  currents. 

463.  The  Inductive  Action  of  a  Temporary 
Magnet. — If  within  the  coil,  a  soft  iron  bar  (or  still 
better,  a  bundle  of  straight,  soft,  iron  wires)  be  placed, 
as  shown  in  Fig.  241,  the  induced  current  may  be  more 


FIG.  241. 

effectively  produced  by  bringing  one  end  of  a  permanent 
magnet  near  the  end  of  the  soft  iron.  In  this  case,  the 
induced  currents  are  due  to  the  varying  magnetism  of  the 
soft  iron,  this  magnetism  being  due,  in  turn,  to  the  in- 
ductive influence  of  the  permanent  magnet.  Thus  we 
see  that  when  the  intensity  of  the  magnetism  of  a 
bar  of  iron  or  steel  is  increased  or  diminished, 
currents  are  induced  in  the  neighboring  coil. 
Similar  effects  may  be  produced  by  moving  one  pole  of 
the  magnet  across  the  face  of  the  coil  from  end  to  end. 


.140 


INDUCED  ELECTRICITY. 


464.  The  Wheel  Armature.— Imagine  the  soft 
iron  bar  in  the  helix  of  Fig.  241  to  be  grooved  and  several 
times  as  long  as  the  helix  through  which  it  passes.  Imag- 
ine the  ends  of  this  bar  to  be  brought  together  so  as  to 

form  a  complete  iron 
ring  carrying  one  helix. 
If  the  number  of  helices 
upon  the  ring  be  in- 
creased to  twelve  we 
shall  have  the  wheel 
armature,  shown,  in  an 
unfinished  condition,  in 
Fig.  242.  If  the  pole 
of  a  magnet  be  passed 
around  the  face  of  this 
wheel,  it  will  pass  twelve 
coils  of  wire  and  induce 
a  current  of  electricity  as  it  approaches  each  coil  and  an 
opposite  current  as  it  leaves  each  coil,  thus  inducing 
twenty-four  currents  for  each  revolution.  Of  course,  it 
makes  no  difference  whether  the  magnet  be  permanent  or 
temporary,  whether  the  pole  of  the  magnet  moves  by  the 
coil  or  the  coil  passes  by  the  pole  of  the  magnet.  Then,  if 
the  magnet  be  fixed  and  the  wheel  turn  upon  its  axis  in 
such  a  way  as  to  carry  its  coils  across  the  end  of  the 
magnet,  we  shall  be  inducing  twenty-four  currents  of 
electricity  for  each  revolution  of  the  wheel.  This  is  what 
happens  in  the  operation  of  a  dynamo-electric  machine. 
When  a  closed  circuit  conductor  moves  in  a  mag- 
netic field  so  as  to  cut  across  the  lines  of  magnetic 
force  (§  433),  an  induced  current  of  electricity  flows 
through  the  conductor  in  on»  direction  while  the 


INDUCED   ELECTRICITY. 


341 


conductor  is  approaching  the  point  of  greatest 
magnetic  intensity  and  in  the  opposite  direction 
while  the  conductor  is  moving  away  from  such 
point  of  maximum  intensity.  The  varying  magnetic 
intensity  of  the  iron  core  of  each  moving  coil  increases 
this  effect  as  explained  in  §  463.  Of  course,  the  number 
of  coils  on  the  armature  may  be  more  or  less  than  twelve, 
or  the  armature  may  be  of  a  form  almost  wholly  different 
from  that  just  described,  but,  in  every  case,  the  principle 
of  its  action  is  as  above  stated.  The  dynamo  represented 
in  Fig.  243  has  only  eight  armature  helices  and  diametric* 
ally  opposite  coils  are  joined  so  as  to  form  four  pairs. 


FIG.  243. 

465.    Dynamo-Electric    Machines. —  In    the 

Brush  dynamo-electric  machine,  represented  in  Fig.  243,  a 
shaft  runs  through  the  machine  from  end  to  end,  carrying 
a,  pulley,  P,  at  one  end,  a  commutator,  c,  at  the  other, 
and  a  wheel  armature,  R,  at  the  middle.  The  armature, 
R,  carries  eight  or  more  helices  of  insulated  wire,  H  H. 


342  INDUCED   ELECTRICITY. 

As  the  shaft  is  turned  by  the  belt  acting  upon  P,  R  and 
c  are  turned  with  it.  As  R  turns  around,  it  carries  the 
eight  coils,  H  H,  rapidly  across  the  poles  of  the  four 
powerful  field  magnets,  M  M. 

As  each  coil  passes  each  pole,  it  necessarily  tra- 
verses the  magnetic  field  and  cuts  across  the  lines 
of  magnetic  force;  consequently,  currents  are  in- 
duced in  the  coil.  These  currents  are  carried  on  insu- 
lated wires  to  the  commutator  rings,  c  c,  where  they  are 
united  in  such  a  way  as  all  to  flow  in  the  same  direction, 
forming  a  continuous  current.  The  electricity  is  taken 
from  the  revolving  commutator,  c  c,  by  the  four  or  more 
fixed,  copper  plates,  i  i,  technically  called  "  brushes,"  then 
carried  down  the  flexible  copper  strips,  s  s,  then  passed 
through  the  insulated  wire  of  the  electro-magnets,  M  M, 
and,  finally,  to  the  +  binding  post.  Thence  the  current 
passes  by  a  wire  -to  the  external  circuit,  e.  g.,  to  an  arc 
lamp  (Fig.  246)  and  from  this  to  a  second  lamp,  and  so  on 
through  all  of  the  lamps  of  the  circuit  and  from  the  last 
lamp  back  to  the  —  binding  post  of  the  dynamo-electric 
machine,  thus  making  the  circuit  complete.  Sixty  or 
more  arc  lamps  in  series  may  be  worked  by  one  of  these 
machines.  No  part  of  the  circuit  of  a  dynamo  should 
have  an  earth  connection.  The  complete  circuit  (except 
through  the  lamp  carbons)  should  be  of  carefully  insu- 
lated wire. 

Dynamo-electric  machines  are  being  rapidly  introduced 
for  purposes  of  electric  lighting,  electro-plating,  motive 
power,  telegraphy,  etc.  They  are  made  in  various  forms, 
but  tfye  principle  underlying  the  action  of  them  all  i&  the 
same  as  that  stated  in  the  last  paragraph.  After  master- 
ing the  action  of  one  dynamo-electric  machine  the  pupil 


INDUCED  ELECTRICITY.  343 

will  have  little  trouble  in  understanding  the  action  of  any 
other  that  he  may  have  a  chance  to  examine.  Dynamo- 
electric  machines  are  often  called  "  dynamos."  A  small, 
hand  power  dynamo,  suitable  for  school  use,  may  be  had 
for  $30  or  more. 

(a.)  In  cases  where  a  high  E.  M.  F.  is  needed  (as  in  arc  electric 
lighting),  the  armature  helices  are  wound  with  many  turns  of  wire 
which  gives  a  high  internal  resistance.  Compare  §  399.  When  a 
smaller  E.  M.  F.  is  wanted  (as  in  direct,  incandescence  electric  light- 
ing or  in  electro-plating),  fewer  turns  of  wire  of  greater  diameter 
are  used.  This  reduces  the  internal  resistance  of  the  dynamo. 
Compare  §  400.  The  E.  M.  F.  will  vary  with  the  strength  of  the 
magnetic  field  and  the  speed  at  which  the  armature  is  revolved. 
Thus,  a  given  dynamo  may  be  run  slowly  for  a  few  lamps  and  at  a 
higher  speed  for  a  greater  number  of  lamps.  In  practice,  however, 
special  automatic  devices  are  generally  provided  for  adapting  the 
E.  M.  F.  to  the  varying  resistances  of  the  external  circuk  without 
changing  the  speed  of  the  dynamo. 

(b.)  If  permanent  magnets  are  used  instead  of  electro-magnets, 
the  machine  is  called  a  magneto -electric  instead  of  a  dynamo-electric 
machine.  Small  magnetos  (armatures  wound  with  long,  thin  wires) 
are  much  used  for  electro-medical  purposes.  The  patient  holds  two 
metallic  handles  connected  with  the  terminals  of  the  instrument 
and  receives  a  rapid  succession  of  shocks  when  the  armature  is 
turned. 

(c.)  If,  instead  of  expending  mechanical  energy  to  turn  the  shaft 
of  the  dynamo  and  thus  produce  an  electric  current,  we  pass  a  strong 
current  of  electricity  through  the  dynamo,  the  shaft  of  the  dynamo 
will  be  turned  in  the  opposite  direction  and  may  be  made  to  drive 
ordinary  machinery  as  an  electric  motor.  In  the  former  case,  we 
convert  mechanical  energy  into  electric  energy  ;  in  the  latter  case, 
we  convert  electric  energy  into  mechanical  energy  (§  473). 


466.  Incandescence  Electric  Lamps.— When 

a  conductor  of  high  resistance  is  heated  to  incandescence 
by  the  passage  of  a  current,  we  have  an  illustration  of  the 
fundamental  principle  of  incandescence  electric  light- 
ing. To  prevent  the  fusion  of  the  conductor,  a  carbon 


344 


INDUCED  ELECTRICITY. 


THE   SWAN  ELECTRIC   LAMP. 


filament,  about  the  size  of  a  horse-hair,  is  used — carbon 
never  having  been  melted.  To  prevent  the  combustion  of 
the  carbon  filament,  it  is  enclosed 
in  a  glass  globe  containing  either 
a  high  vacuum  or  only  some  inert 
gas,  incapable  of  acting  chemic- 
ally upon  the  carbon  at  even  the 
high  temperature  to  which  it  is 
to  be  subjected.  The  ends  of  the 
carbon  are  connected  with  plat- 
inum wires  that  are  fused  into 
and  passed  through  the  glass. 


(a.)  The  filament  is  carbonized  in 
different  ways  and  given  different 
shapes  by  different  inventors.  The 
Edison  carbon  is  made  of  bamboo  fibre 
and  is  in  the  shape  of  an  ordinary  hair 
pin.  The  Swan  carbon  is  made  of 
parchmentized  cotton  thread.  Fig. 
244  represents  the  Swan  incandescence 
lamp  and  is  half  the  actual  size  of  the 
standard  sixteen  candle  power  lamp. 
Incandescence  lamps  are  generally 
operated  abreast,  as  shown  in  Fig.  245, 
being  placed,  as  it  were,  in  little 
bridges  of  wire  connecting  the  two  conductor  "mains."  Thus,  the 
resistance  of  the  circuit  is  reduced  by  the  successive  addition  of  lamps. 

(b.)  The  resistance  of  carbon   is 
lowered  by  heating  the  conductor.       ^,m  ^ 
The  "hot"  resistance  of  an  incan-  If    r    I      I     !     I 

descence  lamp  is  about  |  its  "cold"  9999  9  9 

resistance. 


FIG.  244. 


FIG.  245. 

467.  The  Voltaic  Arc.— 

The  most  brilliant  luminous  effect  of  current  electricity  is 
the  arc  of  an  electric  lamp.  This  lamp  consists  essentially 
of  two  pointed  bars  of  hard  carbon,  generally  copper  coated 


INDUCED   ELECTRICITY. 


345 


(Experiment  78),  placed  end  to  end  in  the  circuit  of  a 
powerful  current.  If  the  ends  of  the  carbons  be  separated 
a  short  distance  while 
the  current  is  passing, 
the  carbon  points  be- 
come intensely  heated 
and  the  current  will 
not  be  interrupted 
thereby.  When  the 
carbons  are  thus 
separated,  their  tips 
glow  with  a  brill- 
iancy which  ex- 
ceeds that  of  any 
other  light  under 
human  control, 
while  the  tempera- 
ture of  the  inter- 
vening arc  is  un- 
equalled' by  any 
other  source  of  ar- 
tificial heat. 

The  mechanism 
shown  in  the  upper 
part  of  Fig.  246,  is  for 
the  purpose  of  auto- 
matically separating  the  carbons  and  "feeding"  them 
together  as  they  are  burned  away  at  their  tips  and  for  the 
purpose  of  cutting  the  lamp  out  of  the  circuit  in  case  of 
any  irregularity  or  accident.  Such  lamps  of  from  one  to 
two  thousand  candle  power  and  requiring  an  expenditure, 
at  the  dynamo,  of  about  one-horse  power  per  lamp  are 


FIG.  246. 


346 


INDUCED   ELECTRICITY. 


now  quite  common.  Lamps  of  a  hundred  thousand  can- 
dle power  have  been  made.  The  current  may  be  furnished 
by  a  battery  of  forty  or  more  Grove's  cells  but,  for  eco- 
nomical reasons,  it  is  almost  universally  supplied  by  a  dy- 
namo-electric machine. 

(a.)  It  is  necessary  to  bring  the  carbons  into  contact  to  start  th« 
light.  The  tips  of  the  carbons  become  intensely  heated  on  account 
of  their  small  area  of  contact  and  the  consequent  high  resistance  at 
that  point.  The  carbon  (and  its  usual  copper  coating)  begins  to 
volatilize.  When  the  carbons  are  separated,  the  current  is  kept  up 
by  this  intervening  layer  of  vapor  and  the  accompanying  disin- 
tegrated matter,  which  act  as  a  conductor.  Arc  lamps  are  generally 

operated  in  series,  so  that  the 
current  passes  in  succession 
through  all  the  lamps  on  the 
circuit.  The  resistance  of  the 
circuit  is  thus  increased  by  the 
successive  addition  of  lamps. 

(&.)  The  constitution  of  the 
voltaic  arc  may  be  studied  by 
projecting  its  image  on  a  screen 
with  a  lens.  Three  parts  will 
be  noticed  : 

1.  The    dazzling  white,    con- 

cave   extremity    of    the 
positive  carbon. 

2.  The  less  brilliant  and  more 

pointed  tip  of  the  nega- 
tive carbon. 

3.  The  globe  shaped  and  beau- 

tifully   colored    aureole 
surrounding  the  whole. 
(c.)  There  is  a  transfer  of  mat- 
ter across  the  arc  in  the  direc 
tion  of  the  current,  the  positive 

carbon  wasting  away  more  than 

FIG.  247.  twice  as  rapidly  as  the  negative. 

Most  of  the  light  of  the  lamp  is 

radiated  from  the  crater  at  the  end  of  the  positive  carbon.  If  the 
arc  be  too  short,  many  of  these  rays  will  be  intercepted  by  the  nega- 
tive (generally  the  lower)  carbon,  thus  lessening  the  efficiency  of  the 


INDUCED   ELECTRICITY.  347 

Jamp.  If  the  arc  become  too  long,  it  will  "flame"  and  much  of 
the  light  thus  be  lost.  If  the  electrodes  be  horizontal,  the  arc  will 
be  curved  upward  by  r.scending  air  currents.  Arc  lamps  are  now 
largely  used  for  lighting  streets,  factories,  stores,  etc.,  many  thou- 
sands having  been  sold  in  every  quarter  of  the  globe  (§  000). 

468.  The  Telephonic  Current. — An  electric  cur- 
rent may  be  induced  in  a  coil  of  insulated  wire  surround- 
ing a  bar  magnet   by   the 

approach  and  withdrawal 
of  a  disc  of  soft  iron.  The 
disc,  a  (Fig.  248),  is  mag- 
netized by  the  inductive 
influence  of  the  magnet,  m, 

(§  435).  The  disc,  thus  magnetized,  reacts  upon  the 
magnet,  m,  and  changes  the  distribution  of  magnetism 
therein.  By  varying  the  distance  between  a  and  m,  the 
successive  changes  in  the  distribution  of  the  magnetism  of 
m  induce  to-and-fro  currents  in  the  surrounding  coil 
(§  463).  When  a  approaches  m,  a  current  flows  in  one 
direction ;  when  it  recedes,  the  current  flows  in  the  oppo- 
site direction. 

469.  The  Telephonic  Circuit.— If  the  wire  sur- 
rounding the  magnet  mentioned  in  the  last  paragraph  be 
continued  to  a  distance  and  then  wound  around  a  second 
bar  magnet,  as  shown  in  Fig.  249,  tbe  currents  induced  at 
M  would  affect  the  magnetism  of  the  bar  at  M'  or  the  in- 
tensity of  its  attraction  for  the  neighboring  disc,  a'. .  A 
vibratory  motion   in  the  disc,   a,  would  induce  electric 
currents  at  M ;  these  currents,  when  transmitted  to  M', 
perhaps  several  miles  distant,  would  affect  the  magnetism 
of  the  bar  there  and  tend  to  produce  exactly  similar  vibra- 


348 


INDUCED   ELECTRICITY. 


tions  in  a'.     "  It  is  as  if  the  close  approach  and  quick 
oscillation  of  the  piece  of  soft  iron  fretted  or  tantalized 


FIG.  249. 

the  magnet  and  sent  a  series  of  electrical  shudders  through 
the  iron  nerve/'  When  the  current  generated  at  M  flows 
in  such  a  direction  as  to  reinforce  the  magnet  at  M',  the 
latter  attracts  a'  more  strongly  than  it  did  before.  When 
the  current  flows  in  the  opposite  direction,  it  weakens  the 
magnetism  of  M't  which  then  attracts  a'  less.  The  disc, 
therefore,  flies  back.  Thus,  the  vibrations  of  a'  are  like 
those  of  a. 

(a.)  We  have  here  the  principle  of  the  telephone,  so  far  as  electric 
action  is  involved.  Further  consideration  of  this  instrument  must 
be  deferred  until  we  have  learned  more  concerning  sound.  (See 
§  505.) 


INDUCED  ELECTRICITY.  349 


EXERCISES. 

1.  A  dynamo  is  feeding  16  arc  lamps,  the  average  resistance  oi 
each  of  which  is  4.56  ohms.     The  internal  resistance  of  the  dynamo 
(i.e.,  of  the  wire  conductors  of  the  armature  and  field  magnets)  is 
10.55  ohms.     What  current  does  the  dynamo  yield  with  an  E.  M.  F. 
of  838.44  volts?  An*.  10.04  amperes. 

2.  If  a  wire  about  18  inches  long  be 
attached  to  one  electrode  of  a  potassium 
dichromate  cell  and  the   other  electrode 
momentarily  touched  with  the  other  end 
of    the    wire,   a  minute   spark  may  be 

noticed  at  the  instant  of  breaking  the  cir-  JTIG< 

cuit.  If  the  wire  be  bent  into  a  scalari- 
form  or  ladder  like  shape  and  the  experiment  repeated,  the  spark  will 
be  greater  than  before.  If  the  form  of  the  external  circuit  be  again 
changed  by  winding  the  wire  into  a  spiral  (as  shown  in  Fig.  250),  the 
spark  will  be  still  greater.  Explain  the  repeated  increase  in  the  spark. 
8.  A  dynamo  is  run  at  450  revolutions,  developing  a  current  of 
9.925  amperes.  This  current  deflects  the  needle  of  a  tangent  gal- 
vanometer, 60°.  (See  Appendix  L.)  When  the  speed  of  the  dynamo 
is  sufficiently  increased,  the  galvanometer  shows  a  deflection  of  74°. 
What  is  the  current  developed  at  the  higher  speed? 

Am.  20  amperes. 

4.  The  current  running  through  the  carbon  filament  of  an  incan 
descence  lamp  was  found  to  be  1  ampere.     The  difference  of  poten- 
tial between  the  two  terminals  of  the  lamp  was  found  to  be  30  volts. 
What  was  the  resistance  of  the  lamp  ? 

5.  A  yard  of  silver  wire  weighs  7.2  grains  and  has  a  resistance  of 
0.3  ohm.     What  is  the  resistance  of  a  foot  of  silver  wire  that  weighs 
one  grain?  Ans.  0.24  ohm. 

6.  If  a  pure  copper  wire  has  a  weight  of  one  grain  and  a  resistance 
of  0.2106  ohms  per  foot  and  a  commercial  copper  wire  has  a  weight 
of  164  grains  and  a  resistance  of  0.547  ohms  per  20  ft.,  what  is  the 
percentage  conductivity  of  the  latter  as  compared  with  pure  copper  ? 

Ans.  93.9  per  cent. 

7.  I  want  to  place,  in  series,  10  incandescence  lamps,  each  of  25 
ohms  resistance  ;  the  line  wire  is  to  be  200  feet  long  and  must  have 
not  more  than  2  per  cent,  of  the  resistance  of  the  lamps.    Determine 
from  the  table  in  Appendix  I  what  size  of  wire  (American  gauge) 
should  be  used.  Ans.  No.  23. 


350  INDUCED  ELECTRICITY. 

8.  I  want  to  place  the  same  lamps  abreast.     The  line  wire  is  to  be 
200  feet  long  and  have  a  resistance  of  not  more  than  2  per  cent,  that 
of  the  lamps.     Determine  from  the  table  what  size  wire  should  be 
used.  Am.  No.  4  (B.  &  S.) 

9.  What  length  of  No.  0000  pure  copper  wire  (B.  &  S.)  will  have  a 
resistance  of  1  ohm?    (See  Appendix  I.)  Am.  19607.84  ft. 

10.  A  dynamo  has  an  E.  M.  F.  of  206  volts  and  an  internal  (or  in 
terpolar)  resistance  of  1.6  ohms.     Find  the  current  strength  when 
the  external  resistance  is  25.4  ohms.  Ans.  7.6  amperes. 

11.  A  dynamo  has  an  internal  resistance  of  2.8  ohms.     The  line 
wire  has  a  resistance  of  1.1  ohms  and  joins  the  dynamo  to  3  arc  lamps 
in  series,  each  lamp  having  a  resistance  3.12  ohms.     Under  such 
conditions,  the  dynamo  develops  a  current  of  14.8  amperes.     What 
is  the  E.  M.  F.  ?  Ans.  196.25  volts. 

12.  A  dynamo,  run  at  a  certain  speed,  gives  an  E.  M.  F.  of  200 
volts.     It  has  an  internal  resistance  of  0.5  ohm.     In  the  external 
circuit  are  3  arc  lamps  in  series,  each  having  a  resistance  of  2.5  ohms. 
The  line  wire  has  a  resistance  of  0.5  ohm.     I  want  a  current  of  just 
25  amperes.     Must  I  increase  or  lessen  the  speed  of  dynamo  ? 

13.  With  an  external  resistance  of  1.14  ohms,  a  dynamo  develops  a 
current  of  81.58  volts  and  29.67  amperes.     What  is  the  internal  re- 
sistance of  the  dynamo  ?  Ans.  1.61  ohms. 

14.  Upon  trial,  it  was  found  that  a  dynamo  that  was  known  to 
have  an  internal  resistance  of  4.58  ohms  developed  a  current  of  157.5 
volts  and  17.5  amperes.     What  was  the  resistance  of  the  external 
circuit?  Ans.  4.42  ohms. 

15.  Three  incandescence  lamps  having  a  resistance  of  39.3  ohms 
each  (when  hot)  were  placed  in  series.     The  total  resistance  of  the 
circuit  outside  of  the  lamps  was  11.2  ohms.     The  current  measured 
1.2  amperes.     What  was  the  E.  M.  F.  ?  Ans.  154.92  volts. 

16.  The  same  lamps  were  placed  in  multiple  arc  with  another 
dynamo.     The  line  wire  was  adjusted  so  that  its  resistance  with  the 
internal  resistance  of  the  machine  was  11.2  ohms  as  before.     The 
current  was  1.2  amperes.     What  was  the  E.  M.  F.? 

Ans.  29.16  volts. 

17.  A  dynamo  supplies  current  for  two  incandescence  lamps  in 
series,  each  having  a  hot  resistance  of  97  ohms.     The  other  resist- 
ances of  the  circuit  amounted  to  12  ohms.     The  current  in  the  first 
lamp  was  1  ampere.     What  was  the  current  carried  by  the  carbon 
filament  of  the  second  lamp  ?    What  was  the  E.  M.  F.  ? 

18.  The  resistance  of  the  normal  arc  of  an  electric  lamp  is  3.8 
ohms.     The  current  strength  is  10  amperes.     What  is  the  difference 
of  potential  between  the  carbon  tips,  Ans.  38  volts. 


INDUCED  ELECTRICITY.  351 

10.  The  resistance  of  the  arc  lamp  above  mentioned,  when  the 
carbons  are  held  together,  is  0.62  ohm.  When  it  is  burning  with 
normal  arc  and  a  10  ampere  current,  what  is  the  difference  of  poten- 
tial between  the  terminals  of  the  lamp  ?  Ans.  44.2  volts. 

HONORARY  PROBLEMS. 

20.  Four  arc  lamps,  with  a  resistance  of  6  ohms  each,  are  joined 
in  series,  150  feet  apart.     The  first  lamp  is  1,500  feet  and  the  last 
is  1,350  feet  from  the  dynamo.     The  line  wire  has  a  conductivity 
of  96  per  cent,  that  of  pure  copper.     Its  resistance  must  not  exceed 
8  per  cent,  of  that  of  the  lamps.     The  resistance  of  a  foot  of  pure 
copper  wire  1  mil  in  diameter  being  9.94  ohms,  what  must  be  the 
diameter  of  the  line  wire  ?  Ans.  133  mils  or  0.133  inch. 

Use  No.  10  wire,  B.  W.  G.  (App.  I). 

21.  Twenty-five  similar  voltaic  cells  having  an  internal  resistance 
of  15  ohms  each  were  joined  in  series,  by  short  and  stout  copper 
wires  to  a  70  ohms  incandescence  lamp  and  produced  a  current  of 
0.112  ampere.     What  would  be  the  strength  of  the  current  sent  by 
a  series  of  30  such  cells  through  a  series  of  2  lamps,  each  of  30  ohms 
resistance?  Ans.  0.118  ampere. 

22.  What  would  have  been  the  strength  of  current  through  the 
two  lamps  if  the  area  of  each  of  the  battery  plates  had  been  doubled, 
all  things  else  remaining  the  same  ?  Ans.  0.2105  ampere. 

23.  I  join  50  arc  lamps  in  series.     Each  lamp  has  a  resistance  of 
4.5  ohms.     The  line  wire  connecting  them  with  the  dynamo  is  3| 
miles  long  and  its  conductivity  is  90  per  cent,  that  of  pure  copper. 
One  tenth  of  the  total  energy  of  the  external  circuit  is  lost  in  heat- 
ing this  line  wire.    What  is  its  diameter,  it  being  assumed  that  1  foot 
of  pure  copper  wire.  1  mil  in  diameter  has  a  resistance  of  9.94  ohms. 

Ans.  90.3  mils. 
Use  No.  11  wire  (B.  &  S.) 


352  INDUCED  ELECTRICITY. 

Recapitulation. — To  be  amplified  by  the  pupil  foi 


review. 


fc  Q 

w  g 

r^ 

*  £ 

ffi  U 


CLOSING. 


BREAKING. 


PRIMARY  CIRCUIT. 


PRIMARY. 


SECONDARY. 


Coils. 


RUHMKORFF. 
EXTRA  CURRENT. 

CHANGE  OF  DISTANCE  OF  PRIMARY  CIRCUIT. 

(Current. 
Circuit. 
PERMANENT,  f 

*•  MAGNETO-ELECTRIC  MACHINES 
f  WHEEL  ARMATURE. 
MAGNETS.  "I  r  Electro-Plating 


Incandescence 
Electric  Light 
ing. 

DYNAMO-ELEC- 
TRIC MACHINES,  \  Arc  Electric 
USED  FOR....        Lighting. 


-TEMPORARY. 


Charging  Stor- 
age Batteries. 


Motive  Power. 
ELECTRIC  MOTORS. 


*AV~ 

ELECTRIC    CURRENTS    AS    RELATED    TO    HEAT 
AND    MECHANICAL    WORK. 

4W.  The  Convertibility  of  Electric  En- 
ergy.— Whenever  an  electric  current  does  work  of  any 
kind,  it  does  it  at  the  expense  of  a  part  "of  its  own  energy. 
Anything  that  increases  the  resistance  of  a  circuit,  decreases 
the  strength  of  the  current  (§  386).  But  such  a  diminu- 
tion may  be  caused  by  a  counter  electromotive  force  set  up 
somewhere  in  the  circuit.  The  E.  M.  F.  of  polarization 
is  an  example  of  the  truth  under  consideration.  When- 
ever a  current  is  used  to  drive  an  electric  motor,  the  action 
of  the  motor  generates  a  back  current  that  diminishes  the 
current  of  the  battery  or  dynamo.  All  of  the  current 
that  is  not  expended  in  some  such  way,  in  exter- 
nal work,  is  dissipated  as  heat.  The  dissipation  may 
be  in  the  battery  (or  dynamo),  in  the  external  circuit  or 
in  both.  The  heat  will  appear  wherever  there  is  resistance. 
If  the  poles  of  a  battery  or  dynamo  be  short  circuited,  most 
of  the  heat  will  be  developed  in  the  battery  or  dynamo. 
If  the  external  circuit  be  a  thin  wire  of  high  resistance,  it 
will  grow  hot  while  the  generator  will  remain  compara- 
tively cool. 


354 


ELECTRICITY  AND   HEAT. 


471.  Joule's  Law. — The  quantity  of  heat  developed 
in  a  conductor  by  the  passage  of  an  electric  current  is 
proportional : — 

(1.)  To  the  resistance  of  the  conductor. 

(2.)  To  the  square  of  the  strength  of  the  current. 

( 3. )  To  the  time  the  current  is  flowing. 

A  current  of  one  ampere  flowing  through  a  resistance 
of  one  ohm,  develops  therein,  per  second,  a  quantity  of  heat 
which  (or  its  mechanical  equivalent)  is  called  a  joule.  It  is 
equal  to  0.7373  of  a  foot-pound  or  to  0.24  of  a  lesser  calorie 
(§  579).  A  lesser  calorie  is,  therefore,  equal  to  4.17  joules. 

These  facts  are  concisely  stated  by  the  following  equa- 
tion, known  as  Joule's  Law : — 

H  =  C*Rt  x  0.24, 

in  which  # represents  the  number  of  lesser  calories;  C,  the 
number  of  amperes ;  R,  the  number  of  ohms  and  t,  the 
number  of  seconds.  In  other  words,  a  current  of  one 
ampere  flowing  through  a  resistance  of  one  ohm 
develops  therein  0.24  of  a  lesser  calorie  per  second. 
Foot-pounds  =C*Rtx  0.737335. 

(a.)  In  investigating  this  subject, 
Joule  used  instruments  on  the  prin- 
ciple indicated  in  Fig.  251,  in  which 
a  thin  wire  joined  to  two  stout  con- 
ductors is  enclosed  within  a  glasa 
vessel  containing  alcohol,  into  which 
a  thermometer  dips.  The  resist- 
ance of  the  wire  being  known,  its 
relation  to  the  other  resistances  may 
be  calculated. 

Experiment  105.— Send  the  cur- 
rent  from   a   few   cells  through   a 
chain  made  of   alternate    links  of 
silver  and  platinum  wires.     The  platinum  links  grow  red-hot  while 


ELECTRICITY  AND  HEAT.  355 

the  silver  links  remain  comparatively  cool.  The  explanation  is  that 
the  specific  resistance  (Appendix  K,  [2])  of  platinum  is  about  six 
times  that  of  silver  and  that  its  specific  heat  is  about  half  as  great ; 
hence  the  rise  of  temperature  in  wires  of  equal  thickness  traversed 
by  the  same  current  is  about  twelve  times  as  great  for  platinum  as 
for  silver. 

472.   Heating  Wires  by  the  Current.  — The 

resistance  of  metals  increases  with  the  temperature.  Con- 
sequently, a  thin  wire  heated  by  the  current  will  resist 
more  and  more  and  grow  hotter  and  hotter  until  it 
loses  heat  by  conduction  and  radiation  into  the  surround- 
ing air  as  rapidly  as  heat  is  supplied  by  the  current. 
Thin  wires  heat  much  more  rapidly  than  thick. 
The  rise  of  temperature  in  different  parts  of  a 
wire  of  uniform  material  hut  varying  diameter 
(the  current  remaining  the  same)  will  he  in- 
versely proportional  to  the  fourth  power  of  the 
diameters. 

(a.)  Suppose  a  wire  at  any  point  to  become  reduced  to  Jidlf  its 
diameter.  The  cross-section  will  have  an  area  \  as  great  as  in  the 
thicker  part.  The  resistance  here  will  be  4  times  as  great,  and  the 
number  of  heat  units  developed  will  be  4  times  as  great  as  in  an 
equal  length  of  the  thicker  wire.  But  4  times  the  amount  of  heat 
spent  on  £  the  amount  of  metal  will  warm  it  to  a  degree  16  times  as 
great  (16  =  24). 

(&.)  A  thin  platinum  wire,  heated  white-hot  by  a  current,  is  some- 
times used  in  surgery,  instead  of  a  knife,  as  it  sears  the  ends  of  the 
severed  blood  vessels  and  thus  prevents  hemorrhage.  Platinum  is 
chosen  on  account  of  its  infusibility,  but  even  platinum*  wires  are 
fused  by  too  strong  a  current.  Carbon  is  the  only  conductor  that 
resists  all  attempts  at  fusion  (§  466). 

(c.)  Sometimes  stout  conducting  wires  are  laid  from  a  battery  at  a 
safe  distance  to  a  fuse  connected  with  a  blast  of  powder  or  other  ex- 
plosive. In  the  fuse,  is  a  thin  platinum  wire,  forming  part  of  the 
electric  circuit.  The  fuse  is  ignited  by  heating  the  platinum  wire 
by  sending  the  current  through  it.  Such  methods  are  frequently 
used  in  the  operations  of  both  peace  and  war. 


356  ELECTRICITY  AND  MOTIVE  POWER. 

473.  Electric  Motors. — An  electric  motor  is  a 
device  for  converting  the  energy  of  an  electric  cur- 
rent into  motive  power  by  means  of  electro-magnets. 
Illustrative  apparatus  of  this  kind  may  be  found  in  many 
school  laboratories  or  will  be  gladly  supplied  by  dealers  in 
philosophical  apparatus.  But  the  best  electric  motors  are  the 
now  common  dynamo  electric  machines  or  slight  modifica- 
tions thereof.     Such  "electro-magnetic  engines  "are  rap- 
idly coming  into  use  for  operating  sewing  machines  and 
other  light  machinery,  the  current  being  supplied  indirectly 
by  a  storage  battery  or  directly  by  a  voltaic  battery  or 
dynamo.     Some  "Electric  Light  and  Power  Companies " 
now  run  such  motors  on  their  arc  light  circuits,  selling 
current  to  some  for  power  and  to  others  for  light.     In 
many  cases  where  it  is  undesirable  to  use  a  steam  engine, 
an  electric  motor  may  be  made  available.     Such  motors, 
up  to  the  capacity  of  40  H.  P.,  are  now  in  the  market. 
Some  of  them  have  been  successfully  and  economically 
used  in  propelling  street  railway  cars. 

474.  Electric   Transmission   of  Power.— A 

water  fall,  perhaps  at  a  point  not  easily  accessible,  may  be 
made  to  turn  a  turbine  or  other  water  wheel,  which  shall 
drive  a  dynamo,  which  shall  generate  a  current,  which 
shall  be  carried  by  wire  to  some  available  point  and  there 
converted-  into  mechanical  power  again  by  means  of  an 
electric  motor.  Thus,  an  otherwise  waste  water-power 
may  be  made  a  source  of  profit.  The  scheme  of  thus  dis- 
tributing part  of  the  power  of  Niagara  over  the  State  of 
New  York  has  been  seriously  considered.  It  may  be  pos- 
sible (as  a  profitable  commercial  undertaking)  to  burn 
cheap  fuel  at  the  coal  mine  for  running  large  stationary 


ELECTRICITY  AND  POWER.  357 

engines  and  thus  deliver  the  power  to  consumers  at  great 
distances. 

475.  The  Watt. — The  electric  unit  of  power  (rate 
of  doing  work)  is  called  a  watt.  A.  watt  is  the  amount 
of  power  conveyed  by  a  current  of  one  ampere 
through  a  difference  of  potential  of  one  volt.  It 
equals  (10"1  x  108  =)  107  ergs  or  ^-g-  horse-power, 

W=C  x  E  =  'E^-  =  C*R9 
±1 

in  which  W  equals  the  number  of  watts;  C,  the  number 
of  amperes ;  E9  the  number  of  volts  and  R,  the  number 
of  ohms. 

For  example,  if  the  difference  of  potential  (Appendix  M, 
[4  «.])  between  the  terminals  of  an  arc  lamp  that  is  sup- 
plied with  a  ten  ampere  current  be  45.8  volts,  how  much 
of  the  power  used  in  driving  the  dynamo  is  consumed  in 
the  lamp  ? 

W*=CxE=10x  45.8  =  458,  the  number  of  watts. 
458  ~  746  =  0.614,  the  number  of  horse-powers. 

(a.)  The  formula  W  —  C  x  E  is  determined  by  the  definition  of 

77T 

the  watt.     From  Ohm's  law,  we  see  that  G  —  — .     Substituting  this 

ET  Etg 

value  of  0,  the  formula  becomes  TF—  —  x  E  =  — ,  as  above.     This 

R  R 

shows  that  the  power  varies  as  the  square  of  the  E.  M.  F.  when  the 
resistance  remains  constant,  or  that  the  power  varies  inversely  as  the 
resistance  when  the  E.  M.  F.  remains  constant. 

(6.)  W=  C  x  E.  But  E  =  C  R.  Substituting  this  value  of  E, 
the  formula  becomes  TF=  C  x  G  R  =  CSR,  as  above.  This  shows 
that  tlie  power  varies  as  the  square  of  the  current  when  the  resistance 
remains  constant  or  that  the  power  varies  as  the  resistance  when  the 
current  remains  constant. 


358  ECONOMY  OF  CONDUCTION. 

476.  Relation  of  Conductors  to  E.  M.  F.— 

This  subject  may  be  well  studied  by  means  of  an  example. 
The  energy  of  a  ten  ampere  current  with  an  E.  M.  F.  of 
fifty  volts  is  equal  to  that  of  a  five  ampere  current  with 
an  E.  M.  F.  of  one  hundred  volts. 

W=  C  x  E=  10  x  50  =  100  x  5  =  500. 

These  equivalent  currents  (500  watts  each),  flowing  through 
similar  wires,  will  develop  widely  different  quantities  of 
heat.  If  we  take  any  convenient  wire,  say  one  of  fifteen 
ohms,  the  heat  developed  in  each  case  will  be  as  follows: 

H=  C2  x  Rb  x  0.24.     (§  471.) 

102  x  15  x  0.24=360,  the  number  of  heat  units  per  second. 
52x15x0.24=  90,  "  " 

.« 
In  other  words,  the  same  electric  energy  develops  only 

one-fourth  as  much  heat  with  the  current  of  high  electro- 
motive force  as  it  does  with  the  current  of  low  E.  M.  F., 
the  same  wire  being  used.  It  is  easily  evident  that  a  great 
saving  in  the  cost  of  conductors  may  be  made  possible  by 
the  use  of  currents  of  high  E.  M.  F.  (See  §  474.)  But 
such  currents  are  more  dangerous  to  handle  and  require 
careful  insulation  and  special  precautions  to  lessen  the 
risk  of  serious  accident. 


ELECTRICITY,  HEAT  AND    WORK.  359 


EXERCISES. 

1.  What  shorter  name  may  be  given  for  a  volt-ampere  ? 

2.  What  electrical  horse-power  is  required  to  send  a  current  of  10 
amperes  through  10  arc  lamps  (in  series)  each  having  a  resistance  ol 
4.476  ohms?  Ana.  6.H.  P. 

3.  How  many  joules  will  be  developed  per  minute  by  a  10  ampere 
current  in  a  lamp  of  4.42  ohms  resistance?          Ana.  26520  joules. 

4.  How  many  calories  will  be  developed  in  a  40  ohm  incandescence 
lamp  by  the  passage  of  a  current  of  1.2  amperes  through  it  for  a 
minute?  Ans.  0.82944  calories. 

5.  Find  the  mechanical  equivalent  (in  foot-pounds)  of  the  work 
done  by  a  5  ampere  current  working  for  a  minute  against  100  ohms 
resistance?  Ans.  110600|  foot-pounds. 

6.  A  30,000  watt  dynamo  develops  an  E.  M.  F.  of  3000  volts. 
What  is  the  current  strength  ?  Ans.  10  amperes. 

7.  How  much  power  is  required  properly  to  operate  an  arc  lamp 
that  has  a  difference  of  potential  of  45.2  volts  between  its  terminals, 
it  having  been  adjusted  for  a  10 ampere  current? 

8.  The  difference,  of  potential  between  the  two  terminals  of  an 
arc  lamp  was  found  to  be  37.7  volts.     A  25  ampere  current  was 
passing  through  the  lamp.     What  is  the  power  consumed  in  the 
lamp?  Ans.  942.5  watts,  or  1|  H.  P. 

9.  A  certain  Edison  incandescence  lamp  has  a  resistance  of  125 
ohms.     The  difference  of  potential  between  the  terminals  of  the 
carbon  is  110  volts,     (a.)  What  is  the  current  strength?    (6.)  What 
amount  of  heat  is  developed  in  the  lamp  per  second  ? 

Ans.  (a.)  0.88  ampere ;  (b.)  23.23  lesser  calories. 

10.  A  Grove  cell  has  an  E.  M.  F.  of  1.9  volts  and  a  resistance  of 
0.4  ohm.     Its  plates  are  joined,  first,  by  a  3  ohms  wire  ;  second,  by 
a  30  ohms  wire,     (a.)  What  is  the  current  in  each  case  ?    (b.)  What 
amount  of  heat  per  second  is  developed  in  each  case  ? 

(a.)  .559  amperes  in  first  case. 


Ans. 


.0625  "  second  case. 

(b.)  .125  joules  "  first  case. 

.00625  "  "  second  case. 
About  80  times  as  much. 


360 


ELECTRICITY,  HEAT  AND    WORK. 


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REVIEW.  361 


REVIEW  QUESTIONS  AHD  EXERCISES. 

1.  (a.)  Give  the  laws  for  pressure  of  liquids  and  (&.)  explain  each 
by  some  fact  or  experiment. 

2.  (a.)  What  is  a  natural  magnet?     (&.)   An  artificial  magnet? 
(c.)  How  does  a  magnet  behave  toward  soft  iron?     (d.)  How  does 
one  magnet  behave  toward  another  magnet  ? 

3.  Give  the  facts  in  regard  to  the  variation  of  the  magnetic  needle. 

4.  (a.)  What  are  conductors  in  electricity  ?    (b.)  In  what  ways  may 
electrical  separation  be  effected? 

5.  (a.)  What  conditions  in  the  construction  and  erection  of  light- 
ning-rods are  necessary  to  insure  safety  from  lightning  ?     (6.)  Give 
the  elements  of  a  simple  voltaic  cell  and  (c.)  the  electric  condition  of 
those  elements  within  and  without  the  liquid. 

6.  (a.)  A  body  weighs  at  the  surface  of  the  earth  1014  Ib.  ;  what 
would  it  weigh  1200  miles  above  the  surface?    (&.)  Give  the  velocity 
of  water  issuing  from  an  orifice,  under  a  head  of  81  feet,    (c.)  If  5 
quarts  of  water  weigh  as  much  as  7  of  alcohol,  what  is  the  specific 
gravity  of  the  alcohol  ? 

7.  Find  the  kinetic  energy  of  a  25  Ib.  ball  that  has  fallen  3600  feet 
in  vacuo.  Am.  90,000  foot-pounds. 

8.  Give  the  fundamental  principle  of  Mechanics  and  illustrate  its 
application  by  one  of  the  mechanical  powers. 

9.  (a.)  Over  how  high  a  ridge  can  you  continuously  carry  water 
in  a  siphon,  where  the  minimum  range  of  the  barometer  is  27  inches? 
(&.)  Explain. 

10.  (a.)  What  is  specific  gravity?  (&.)  How  do  you  find  that  of 
solids?    (c.)  What  principle  is  involved  in  your  method  ? 

11.  (a.)   How  much  water  per  hour  will  be  delivered  from  an 
orifice  of  2  inches  area,  25  feet  below  the  surface  of  a  tank  kept  full 
of  water,  not  allowing  for  resistance?    (&.)  Give  the  law  of  magnetic 
attraction  and  repulsion.  Ans.  14,998.44  gal. 

12.  (a.}  State  what  you  have  been  taught  concerning  the  dipping 
needle.     (&.)  Define  and  illustrate  magnetic  induction. 

13.  (a.)  Give  the  law  of  electric  attraction  and  repulsion  and  illus- 
trate by  the  pith-ball  electroscope.     (6.)  Define  conductors  and  non- 
conductors, electrics  and  non-electrics,    (c.)  Illustrate  by  an  example 
of  each. 

14.  (a.}  Explain  (by  figures)  electric  induction,     (b.)  Explain  the 
charging  of  a  Leyden  jar.     (c.)  When  charged,  what  is  the  electric 
condition  of  the  outside  and  inside  of  the  jar  ? 


362  REVIEW, 

15.  (a.}  Give  the  sources  of  atmospheric  electricity  and  (&.)  the 
effects  of  lightning. 

16.  (a.)  What  is   the  effect  of  breaking  a  magnet?    (6.)  Give  a 
theory  of  magnetism  that  is  competent  to  account  for  the  properties 
of  magnets,  broken  or  unbroken. 

17.  (a.)  How  do  soft  iron  and  tempered  steel  differ  as  to  suscep- 
tibility to  magnetism  ?     (6.)  Describe  one  method  of  magnetizing  a 
steel  bar. 

18.  The  influence  of  the    earth's  magnetism  upon   a  magnetic 
needle  is  merely   directive,     (a.)   Explain    what   this   means.     (&.) 
Show  why  it  is  so. 

19.  (a.)  What  is   meant  by  electromotive   force?     (b.)   Describe 
Grove's  battery  and  its  mode  of  action,     (c.)  Why  are  battery  zincs 
generally  amalgamated  ? 

20.  (a.)  Describe  Oersted's  apparatus  and  (6.)    tell  what  its  use 
teaches,      (c.)   Describe  the  construction  of   the  astatic  galvanom- 
eter. 

21.  (a.)  Describe  an  electro-magnet  and  (&.)  tell  what  its  advan- 
tages are.     (c.)  State  the  principle  of  the  electric  telegraph. 

22.  (a.)  Describe  a  RuhmkorfFs  coil  and  (&.)  explain  its  action. 

23.  (a.)  Define  electrolysis  and  electrolyte.     (&.)  Describe  the  elec- 
trolysis of  water,     (c.)  Give  a  clear  account  of  some  branch  of  elec- 
tro-metallurgy,   (d.)  What  is  meant  by  the  terms  electropositive  and 
electro-negative  ? 

24.  («.)  Define  physics.     (&.)  Name  and  define  the  three  conditions 
of  matter,     (e.)  What  do  you  understand  by  energy?    (d.)  Explain 
what  is  meant  by  foot-pound. 

25.  (a.)  What  condition  of  the  atmosphere  is  desirable  for  experi- 
ments in    frictional   electricity?     (&.)  Why?    (c.)   How  could   you 
show,   experimentally,  that  there  are  two  opposite  kinds  of  elec- 
tricity ? 

26.  (a.)  Describe  the  experiment  with  Faraday's  bag  and  (6.)  state 
what  it  teaches,     (c.)  Describe  the  dielectric  machine  and  (d.)  ex- 
plain its  action. 

27.  In  an  air-pump,  the  capacity  cf  the  cylinder  is  one-fourth  that 
of  the  receiver.     Under  ordinary  atmospheric  conditions,  they  to- 
gether contain  62  grains  of  air.     Find  the  capacity  (a.)  of  the  re- 
ceiver, (&.)  of  the  cylinder.     After  5  strokes  of  the  piston,  (c.)  how 
many  grains  of  air  would  be  left  in  the  receiver?    What  would  be 
its  tension  (d.)  in  pounds  per  square  inch  ?    (e.)  In  Kg.  per  sq.  cm.  ? 
(/.)  In  inches  of  mercury?  Ana.  («.)  827.68  g. 

28.  (a.)  Supposing  we  had  two  Leyden  jars,  one  charged  on  the 
inside  with  positive  electricity  and  the  other  with  negative  on  the 


363 


inside  ;  the  two  jars  being  insulated,  can  the  jars  be  fully  discharged 
by  connecting  the  inner  coats?    (b.)  Give  reasons  for  your  answer. 

29.  In  a  vessel  having  the  dimensions  of  a  cubic  foot,  sulphuric 
acid  (sp.  gr.  =  1.83)  stands  eight  inches  high  ;  give  the  pressure  on 
the  bottom  and  each  side. 

30.  The  lever  of  a  hydrostatic  press  is  six  feet  long,  the  fulcrum 
being  at  the  end  and  one  foot  from  the  piston  rod.     The  diameter  of 
the  tube  is  one  inch  ;  that  of  the  cylinder,  ten  inches.    The  power  is 
25  Ib.  ;  give  the  effect.     (See  Appendix  A.) 

31.  Find  the  joint  resistance  of  three  conductors  of  10,  12  and  18 
ohms  arranged  in  multiple  arc.  Ans.  4.18  ohms. 

32.  (a.)   Define  equilibrium  and  its  kinds.     (&.)    Give  examples. 
(c.)  How  does  the  centre  of  gravity  of  any  system,  acted  upon  by 
an  exterior  force,  move  ?    (d.)  Give  an  example. 

33.  (a.)  Figure  a  simple  barometer.     (&.)  Explain  why  the  mer- 
cury stands  above  its  level,     (c.)  What  atmospheric  pressure  will 
sustain  a  column  of  mercury  24  inches  high  ? 

34.  (a.}  How  is  it  proved  that  air  has  weight?    (b.)  What  is  the 
weight  of  air  in  a  room  30  feet  long,  20  feet  wide  and  10  feet  high. 

35.  When  a  1000  gram  flask,  containing  700  g.  of  water,  was  filled 
with  the  fragments  of  a  mineral,   it  weighed   1450  g.     Give  the 
specific  gravity  of  the  mineral.  Ans.  2.5. 

36.  A  tank  measuring  1  meter  each  way  is  filled  with  water  : 
what  will  be  the  pressure  on  the  bottom  and  sides  ? 

37.  (a.)  What  is   meant  by   kinetic  energy?     (b.)    By   potential 
energy  ? 

38.  Two  inelastic  bodies  are  moving  in  opposite  directions,  one 
weighing  31  grams  and  having  a  velocity  of  24  meters  per  second, 
the  other  weighing  22  grams  and  having  a  velocity  of  18  meters 
per  second:    what  is  the  united  energy  (a.)  before   and  (6.)  after 
impact?  Ans.  (a.)  1.27;  (6.)  0.116  kilogrammeters. 

39.  Regarding  the  same  bodies  as  moving  in  the  same  direction, 
what  would  be  the  energy  (a.)  before  and  (b.)  after  impact  ? 

40.  (a.)  Draw  a  simple  figure  showing  the  essential  parts  of  an 
air-pump  and  (b.)  explain  the  process  of  forming  a  vacuum,     (c.)  If 
the  capacity  of  the  barrel  be  £  that  of  the  receiver,  how  much  air 
will  remain  in  the  receiver  at  the  end  of  the  fourth  stroke  of  the 
piston  ?  and  (d.)  what  would  be  its  elastic  force  compared  with  that 
of  the  external  air  ?  Ans.  (d.)  fff. 

41.  The  current  of  a  Grove's  battery  with  a  certain  resistance  in  the 
circuit  is  known  to  be  $  ampere.     Passing  this  current  through  a 
sine  galvanometer,  the  coils  had  to  be  turned  9°  to  bring  them  par- 
allel with  the  needle.    (See  Appendix  L  [2]).    Some  of  the  resistance 


364  REVIEW. 

being  removed,  it  is  found  that  the  coils  have  to  be  turned  70°  to 
bring  them  parallel.     What  is  the  current  in  the  latter  case? 

Ans.  1  ampere. 

42.  If  a  positively  electrified  ball  be  hung  at  the  centre  of  a  room, 
its  charge  will  attract  an  equal  amount  of  —  electricity  to  the  walls 
of  the  room.     To  what  common  piece  of  physical  apparatus  is  this 
arrangement  analogous  ? 

43.  What  length  of  No.  6  pure  copper  wire  (B.  &  S.)  will  have  a 
resistance  of  1  ohm?    (See  Appendix  I.)  Ans.  2433.09  ft. 

44  If  a  foot  of  pure  copper  wire  weighing  1  grain  has  a  resistance 
of  0.2106  ohm  and  20  feet  of  commercial  copper  wire  weighing  150 
grains  has  a  resistance  of  0.613  ohms,  what  is  the  percentage  con- 
ductivity of  the  latter  as  compared  with  pure  copper  ? 

Ans.  91.6  per  cent. 

45.  Sketch  an  arrangement  by  which  a  single  line  of  wire  can  be 
used  by  an  operator  at  either  end  to  signal  to  the  other  ;  the  condi- 
tion of  working  being  that  whenever  either  operator  is  not  sending 
a  message,  his  instrument  shall  be  in  circuit  with  the   line  wire 
and  out  o/' circuit  with  the  battery  at  his   end. 

46.  Calculate,  by  Joule's  law,  the  number  of  heat  units  developed 
in  a  wire  whose  resistance  is  4  ohms  when  a  steady  current  of  0.14 
ampere  is  passed  through  it  for  ten  minutes.  Ans.  11.2  units  of  heat. 

47.  A  dynamo  has  an  E.  M.  F.  of  839  volts  and  an  internal  (or  in- 
terpolar)  resistance  of  10.9  ohms.     Find  the  current  strength  when 
the  external  resistance  is  73  ohms.  Ans.  10  amperes. 

48.  I  have  48  cells,  each  of  1.2  volts  E.  M.  F.  and  each  of  2  ohms 
internal  resistance.    What  is  the  best  way  of  grouping  them  together 
when  it  is  desired  to  send  the  strongest  possible  current  through  a 
circuit  whose  resistance  is  12 ohms?  Ans.  Group  them  three  abreast. 

49.  The  current  from  a  certain  dynamo  (E.  M.  F.  =  839.02  volts) 
was  sent  through  a  series  of  16  arc  lamps  each  having  a  resistance 
of  4.51  ohms.     The  line  wire  had  a  resistance  of  0.8  ohm.     The 
current  measured  10.04  amperes.     What  was  the  resistance  of  the 
dynamo?  Ans.  10.61  ohms. 

50.  Immediately  after  the  discharge  of  a  Leyden  jar,  the  potential 
of  its  knob  is  zero.     It,  however,  begins  to  rise  and  soon  has  a  value 
that  is  a  considerable  part  of  the  potential  before  discharge  and  with 
the  same  sign.     Explain  this. 

51.  What  three  varieties  of  energy  appear  when  a  Leyden  jar  is 
discharged  ? 

52.  How  many  heat  units  (calories)  will  be  developed  by  a  10  am- 
pere current  flowing  through  a  coil  of  50  ohms  resistance  in  a  quar- 
ter of  an  hour  ?  Ans.  1,080  calories. 


REVIEW.  365 

53.  A  current  of  9  amperes  worked  an  electric  arc  light  and  on 
measuring  the  difference  of  potential  between  the  two  carbons  by 
an   electrometer  it  was  found  to  be   140  volts.      What  was  the 
amount  of  power  absorbed  in  the  arc?  Ans.  1.69  H.  P. 

54.  If  the  cells  represented  in  Fig.  252 
have  each  an  internal  resistance  of  4  ohms, 
what  is  the  resistance  of  the  external  cir- 
cuit, G,  if  the  battery  is  working  at  its  great- 
est possible  efficiency?          Ans.  6  ohms. 

55.  The  same  strength  of  current  that 
will  heat  an  inch  of  platinum  wire  to  white- 
ness will  similarly  heat  a  yard  of  the  same 
wire.     Explain  why  it  is  necessary  to  use 
more  cells  thus  to  heat  a  yard  than  it  does 
to  heat  an  inch  of  the  wire. 

56.  Five  Daniel  cells,  each  with  an  E.  M.  pIG    252. 
F.  or  L.i  volts  and  an  internal  resistance  of 

2.2  ohms  are  joined  in  series.  The  external  circuit  consists  of  16743 
feet  of  No.  14  copper  wire  (B.  &  S.)  (See  Appendix  I.)  (a.)  What 
is  the  resistance  of  the  external  circuit?  (6.)  What  is  the  current 
strength?  Ans.  (6.)  0.1  ampere. 

57.  Show  that  with  an  unlimited  number  of  cells  like  that  just 
described,  joined  in  series,  the  current  cannot  exceed  0.5  amperes. 

58.  What  is  the  total  energy  of  the  current  of  the  dynamo,  operated 
as  described  in  Exercise  1,  page  349  ?  ^g    ( 8417.94  watts. 

(11.28  horse-power. 

59.  Explain  the  use  and  construction  of  a  relay. 

60.  Suppose  1000  incandescence  lamps  to  be  placed  parallel  in  the 
circuit  of  a  dynamo.     Each  lamp  has  a  hot  resistance  of  50  ohms 
and  requires  a  current  of  1  ampere,     (a.)  What  will  be  the  current 
strength  developed  by  the  dynamo?    (6.)  What  is  the  resistance  of 
the  lamp  circuit,  ignoring  the  resistance  of  the  leading  \vires  ?    (e.) 
What  is  the  necessary  difference  of  potential  between  the  binding 
posts  of  the  dynamo  ?    (d )  If  the  resistance  of  the  dynamo  itself  is 
0.005  ohm,  what  is  the  total  E.  M.  F.  ?     (e.)  How  many  watts  will  be 
expended  in  each  lamp?     (/.)  If  500  of  the  lamps  be  turned  off 
(open  circuited),  what  will  the  resistance  of  the  lamp  circuit  become  ? 
(g.)  If  the  E.  M.  F.  of  the  dynamo  be  kept  constant  by  change  of 
speed  or  otherwise,  what  will   be   the   current  developed  by  the 
dynamo  with  the  500  lamps?    (h.)  What  will  be  the  current  then, 
supplied  to  each  lamp  ? 

Ans.  (a.)  1000  amperes;  (&.)  0.05  ohm  ;  (c.)  50  volts  ;  (d.)  55  volts; 
(e-)  50;  (/.)  0.1  ohm ;  (#.)  523.81  amperes;  (h.)  1.047  amperes, 


3G6  REVIEW. 


HONORARY   PROBLEMS. 

61.  Two  incandescence  lamps  with  resistances  of  16.9  and  32  ohms 
respectively  were  joined  in  series  with  a  series  of  40  similar  voltaic 
cells  having  a  total  resistance  of  20  ohms.     The  current  measured 
1.16  amperes.     What  will  be  the  strength  of  current  that  a  series  of 
60  such  cells  will  send  through  a  series  of  four  lamps  having  resist- 
ances of  16.9,  82,  20  and  16  ohms  respectively  ? 

Ans.  1.043  amperes. 

62.  What  would  have  been  the  strength  of  current  in  this  case  if 
the  area  of  the  battery  plates  had  been  doubled,  all  things  else  re- 
maining the  same  ?  Ans.  1.2  amperes. 

63.  It  required  15.3  H.  P.  to  drive  a  certain  dynamo  that  had  a 
resistance   of  10.5  ohms   and  developed  a  current  of  10  amperes 
through  an  external  resistance  of  73  ohms.     (The  "  duty  "  of  a  dy- 
namo is  the  ratio  between  the  total  electrical  energy  developed  and 
the  work  performed  in  turning  the  armature  in  the  magnetic  field). 
What  is  the  duty  of  the  dynamo  in  question  ?      Ans.  73  per  cent. 

64.  The  "  commercial  efficiency  "  of  a  dynamo  is  the  ratio  be- 
tween the  electrical  energy  appearing  in  the  external  circuit  and  the 
work  performed  in  turning  the  armature  in  the  magnetic  field.    The 
energy  expended  in  any  part  of  the  circuit  will,  of  course,  depend 
upon  the  resistances  of  that  part  and  of  the  whole  circuit.     What  is 
the  commercial  efficiency  of  the  dynamo  above  mentioned  ? 

Ans.  64  per  cent. 


VII. 


SOUND. 


ECTJON  I. 


V. 

NATURE,  REFRACTION  AND  REFLECTION 
OF  SOUND. 

477.  Definition  of  Sound. — Sound  is  the  mode 
of  motion  that  is  capable  of  affecting  the  auditory 
nerve. 

(a.)  The  word  sound  is  used  in  two  different  senses.  It  is  often 
used  to  designate  a  sensation  caused  by  waves  of  air  beating  upon 
the  organ  of  hearing  ;  it  is  also  used  to  designate  these  aerial  waves 
themselves.  The  former  meaning  refers  to  a  physiological  or 
psychological  process  ;  the  latter  to  a  physical  phenomenon.  If 
every  living  creature  were  deaf  there  could  be  no  sound  in  the 
former  sense,  while  in  the  latter  sense  the  sound  would  exist  but 
would  be  unheard.  The  definition  above  considers  sound  in  the 
physical  sense  only. 

478.  Umlulations.  —  In  beginning  the  study  of 
acoustics,  ic  is  very  important  to  acquire  a  clear  idea  of 
the  nature  of  undulatory  motion.     When  a  person  sees 
waves  approaching  the  shore  of  a  lake  or  ocean,  there 
arises  the  idea  of  an  onward  movement  of  great  masses  of 
water.     But  if  the  observer  give  his  attention  to  a  piece  of 
wood  floating  upon  the  water,  he  will  notice  that  it  merely 


368  NATURE   OF  SOUND. 

rises  and  falls  without  approaching  the  shore.  He  may 
thus  be  enabled  to  correct  his  erroneous  idea  of  the  onward 
motion  of  the  water.  Again,  he  may  stand  beside  a  field 
of  ripening  grain  and,  as  the  breezes  blow,  he  will  see  a 
series  of  waves  pass  before  him.  But  if  he  observe  care- 
fully and  reflect,  he  will  see  clearly  that  there  is  no  move- 
ment of  matter  from  one  side  of  the  field  to  the  other ;  the 
grain-ladened  stalks  merely  bow  and  raise  their  heads. 
Most  persons  are  familiar  with  similar  wave  movements  in 
ropes,  chains  and  carpets.  Each  material  particle  has 
a  motion,  but  that  motion  is  vibratory,  not  progres- 
sive. The  only  thing  that  has  an  onward  movement 
is  the  pulse  or  wave,  which  is  only  a  form  or  change 
in  the  relative  positions  of  the  particles  of  the  un- 
dulating substance. 

(a.)  The  motion  of  the  wave  must  be  clearly  distinguished  from 
the  motion  of  particles  which  constitute  the  wave.  The  wave  may 
travel  to  a  great  distance ;  the  journey  of  the  individual  particle  is 
very  limited. 

479.  Wave  Period. — When  a  medium  is  traversed 
by  a  series  of  similar  waves,  each  particle  is  in  a  state  of 
continued   vibration.     These   vibrations    are    alike,   they 
being  as  truly  isochronous  (§  143)  as  those  of  the  pen- 
dulum.    The  time   required  for  a  complete   vibra- 
tion  is  called   ttie   period,  and    is   th&  same  for 
all  the  particles. 

480.  Wave  Length. — In  such  a  series  of  similar 
waves,  measuring  in  the  direction  in  which  the  waves  are 
travelling,  the  distance  from  any  vibrating  particle  to 
the  next  particle  that  is  in  the  same  relative  posi- 
tion or  "  phase  "  is  called  a  wave  length.    In  the  case 


NATURE   OF  SOUND. 


369 


of  water  waves,  the  distance  from  one  crest  to  the  next  is 
a  wave  length.     (See  First  Prin.  Nat.  Phil,  §  321,  a.) 

481.  Amplitude. — Amplitude  means  the   dis- 
tance between  the  extreme  positions  of  the  vibrating 
particle,  or  the  length  of  its  journey.     As  in  the  case  of 
the  pendulum,  amplitude  and  period  are  independent  of 
each  other.    Amplitude  is  also  independent  of  wave  length. 

482.  Relation  of  Period,  Wave  Length  and 
Velocity. — During  one  period  there  will  be  one  com- 
plete vibration,  and  the  wave  will  advance  one  wave  length. 
The  velocity  of  the  wave  may  be  found  by  multiplying  the 
wave  length  by  the  number  of  vibrations  per  second. 
Conversely,  the  wave  length  may  be  found  by  divid- 
ing the  velocity  by  the  number  of  vibrations. 

483.  Cause  of  Sound.— Ml  sound  may  be  traced 
to  the  vibrations  of  some  material  body.     When  a 

bell  is  struck,  the  edges  of  the 
bell  are  set  in  rapid  vibration, 
as  may  be  seen  by  holding  a 
card  or  finger  nail  lightly  upon 
the  edge.  The  particles  of  the 
bell  strike  the  adjacent  parti- 
cles of  air,  these  pass  the 
motion  thus  received  on  to  the 
air  particles  next  beyond,  and 
these  to  those  beyond. 

(a.)  That  sound  is  due  to  vibra- 
tory motion  may  be  shown  by  nu- 
merous experiments.     Holding  one 
end  of  a  straight  spring,  as  a  hick- 
FIG.  253.  ory  stick,  in  a  vise,  pull  the  free 


»'  3) 


370  NATURE  OF  SOUND. 

end  to  one  side  and  let  it  go.  Elasticity  will  return  it  to  its  position 
of  rest,  kinetic  energy  will  carry  it  beyond,  and  so  on,  a  vibratory 
motion  being  thus  produced.  When  the  spring  is  long,  the  vibra- 
tions may  be  seen.  By  lowering  the  spring  in  the  vise,  the  vibrating 
part  is  shortened,  the  vibrations  reduced  in  amplitude  and  increased 
in  rapidity.  As  the  spring  is  shortened,  the  vibrations  become 
invisible  but  audible,  showing  that  a  sufficiently  rapid  vibratory 
\notion  may  produce  a  sound. 

(&.)  Suspend  a  pith  ball  by  a  thread  so  that  it  shall  hang  lightly 
against  one  prong  of  a  tuning-fork.  When  the  fork  is  sounded,  the 
pith  ball  will  be  thrown  off  by  the  vibrations  of  the  prongs.  Other 
illustrations  of  the  same  truth  will  be  observed  as  we  go  on. 

(c.)  The  vibrations  of  a  tuning-fork  may  be  represented  in  the 
following  manner :  A  glass  plate  which  has  been  blackened  by 
holding  it  in  a  petroleum  flame  is  arranged  so  as  to  slide  easily  in 
the  grooved  frame  F.  A  pointed  piece  of  metal  is  attached  to  one 


FIG.  254. 

of  the  prongs  of  the  fork.  When  the  fork  is  made  to  vibrate,  the 
point  placed  against  the  smoked  plate  and  the  plate  drawn  along 
rapidly  in  the  grooves,  the  point  traces  on  the  glass  an  undulating 
line  which  represents  fairly  the  vibratory  movement  of  the  prong. 

484.  Propagation  of  Sound. — Sound  is  ordi- 
narily propagated  through  the  air.  Tracing  the  sound 
from  its  source  to  the  ear  of  the  hearer,  we  may  say  that 
the  first  layer  of  air  is  struck  by  the  vibrating  body.  The 
particles  of  this  layer  give  their  motion  to  the  particles  of 
the  next  layer,  and  so  on  until  the  particles  of  the  last 
'ayer  strike  upon  the  drum  of  the  ear. 

(a.)  This  idea  is  beautifully  illustrated  by  Prof.  Tyndall.    He 


NATURE  OF  SOUND. 


371 


imagines  five  boys  placed  in  a  row  as  shown  in  Fig.  255.  "  I  sud- 
denly push  A  ;  A  pushes  B  and  regains  his  upright  position  ;  B 
pushes  0 ;  0  pushes 
D  ;  D  pushes  E ; 
each  boy  after  the 
transmission  of  the 
push,  becoming  him- 
self erect.  E,  hav- 
ing nobody  in  front, 
is  thrown  forward. 
Had  he  been  stand- 
ing on  the  edge  of 
a  precipice  he  would 

have  fallen  over;  had  FiG  255. 

he  stood  in  contact 

with  a  window,  he  would  have  broken  the  glass ;  had  he  been  close 
to  a  drum-head,  he  would  have  shaken  the  drum.  We  could  thus 
transmit  a  push  through  a  row  of  a  hundred  boys,  each  particular 
boy,  however,  only  swaying  to  and  fro.  Thus  also  we  send  sound 
through  the  air,  and  shake  the  drum  of  a  distant  ear,  while  each 
particular  particle  of  the  air  concerned  in  the  transmission  of  the  pulse 
makes  only  a  small  oscillation."  (See  First  Prin.,  Exps.  141-144.) 

485.  Sound  Waves. — The  layers  of  air  are  crowded 
more  closely  together  by  each  outward  vibration  of  the 


m 


188! 


FIG.  256, 

sounding  body;  a  condensation  of  the  air  is  thus  produced 
As  the  sonorous  body  vibrates  in  the  opposite  direction, 


372 


NATURE  OF  SOUND. 


the  nearest  layer  of  air  particles  follows  it;  a  rarefaction 
of  the  air  is  thus  produced.  A  sound  wave,  therefore, 
consists  of  two  parts,  a  condensation  and  a  rarefac- 
tion. The  motion  of  any  air  particle  is  backward  and 
forward  in  the  line  of  propagation,  and  not  "  up  and  down  " 
across  that  line,  as  in  the  case  of  water  waves.  A  series  ol 
complete  sound  waves  consists  of  alternate  condensations 
and  rarefactions  in  the  form  of  continually  increasing 
spherical  shells,  at  the  common  centre  of  which  is  the 
sounding  body.  Any  line  of  propagation  of  the  sound 
would  be  a  radius  of  the  sphere. 

486.  Sound  Media. — The  air  particles  impart  their 
motion  to  other  particles  because  of  their  elasticity.  Any 
elastic  substance  may  become  the  medium  for  the 
transmission  of  sound,  but  such  a  medium  is  neces- 
sary. The  elasticity  of  a  body 
may  be  measured  by  the  re- 
sistance it  opposes  to  compres- 
sion. The  less  the  compres- 
sibility, the 
greater  the 
elasticity. 


FIG. 


(a.)  That  sound 
is  not  transmit- 
ted in  a  vacuum 
is  shown  as  fol- 

lows:  A  larSe 
glass  globe,  pro- 
vided with  a  stop-cock,  contains  a 
small  bell  suspended  by  a  thread. 
When  the  air  is  pumped  from  the 
globe  and  the  globe  shaken,  no 
sound  is  heard,  although  the  clap- 
per of  the  bell  is  seen  to  strike 


FIG.  258. 


NATURE  OF  SOUND.  373 

against  the  bell.    Readmitting  the  air,  and  again  shaking  the  globe, 
the  sound  is  plainly  heard.     (See  Fig.  257.) 

(6.)  A  small  music  box,  or  a  clock-work  arrangement  for  striking 
a  bell  (Fig.  258),  may  be  supported  upon  a  thick  cushion  of  felt  or 
cotton-batting,  and  placed  under  the  capped  receiver  of  an  air-pump 
When  the  receiver  is  exhausted,  and  the  machinery  started  by  the 
rod  g,  the  motion  may  be  seen  but  hardly  any  sound  will  be  heard. 
If  the  support  were  perfectly  inelastic  and  the  exhaustion  complete, 
no  sound  would  be  audible.  The  experiment  may  be  made  more 
perfect  by  filling  the  exhausted  receiver  with  hydrogen  and  again 
exhausting  the  gas.  (See  First  Prin.  Nat.  Phil,  Exps.  146-148.) 

487.  Velocity  of  Sound  in  Air.— It  is  a  familiar 
fact  that  the  transmission  of  sound  is  not  instantaneous. 
The  blow  of  a  hammer  is  often  seen  several  second  before 
the  consequent  sound  is  heard ;  steam  escaping  from  the 
whistle  of  a  distant  locomotive  becomes  visible  before  the 
shrill  scream  is  audible;  the  lightning  precedes  the  thunder. 
As  we  shall  see  further  on,  the  time  required  for  the 
propagation  of  light  through  terrestrial  distances  is  inap- 
preciable.    Hence  the  interval  between  the  two  sensations 
of  seeing  and  hearing  is  required  for  the  transmission  of 
the  sound.    This  interval  being  observed  and  the  distance 
being  known,  the  velocity  is  easily  computed.     By  such 
means  it  has  been  found  that  the  velocity  of  sound  in 
air  at  the  freezing  temperature  is  about  332  m.,  or 
1090  ft.  per  second.    There  is  some  reason  for  believing 
that  very  loud  sounds  travel  somewhat  more  rapidly  than 
sounds  of  ordinary  loudness.     "With  this  exception  it  may 
be  said  that,  in  a  given  medium,  all  sounds  travel  with  the 
same  velocity. 

488.  Velocity  in  Other  Media.— The  velocity 
of    sound    depends    upon    two    considerations — the 
elasticity  and  the  density  of  the  medium.    It  varies 
directly  as  fijie  square  root  of  the  elasticity,  and 


374  NATURE  OF  SOUND. 

inversely  as  the  square  root  of  the  density.  At  the 
freezing  temperature,  sound  travels  through  oxygen  with  a 
velocity  of  1040  feet,  and  through  hydrogen  with  a  velocity 
of  4164  feet  per  second. 


•-VS 


(a.)  It  is  a  very  common  mistake  to  think  that  an  increase  of 
density  causes  an  increase  of  velocity.  It  is  known,  e.g.,  that  sound 
travels  more  rapidiy  in  water  than  in  air  ;  that  water  is  more  dense 
than  air ;  hence,  say  the  superficial,  sound  travels  most  rapidly  in 
the  densest  bodies.  It  does  not  follow.  Other  things  being  equal, 
the  denser  the  medium,  the  less  the  velocity  of  the  motion.  A  little 
reflection  will  show  that  this  must  be  so ;  experiments  will  verify 
the  conclusion.  In  wave  motion,  the  particles  of  the  medium  con- 
stitute the  thing  that  is  moved.  With  a  given  expenditure  of  energy, 
a  number  of  light  particles  is  moved  more  rapidly  than  an  equal 
number  of  heavy  particles  (§  157). 

489.  Effect  of  Temperature  Upon  Velocity. 

— An  increase  of  the  temperature  of  the  air  increases  its 
elasticity  and  decreases  its  density.  We  might,  therefore, 
expect  sound  to  travel  more  rapidly  in  warm  than  in  cold 
air.  Experiment  confirms  the  conclusion.  There  is  an 
added  velocity  of  about  1.12  feet  for  every  Fah- 
renheit degree,  or  of  about  2  feet  for  every  centi- 
grade degree  of  increase  of  temperature.  (The 
freezing  temperature  is  32°  F,  or  0°  0. ) 

490.  Momentary  and  Continuous   Sounds. 

—A  sound  may  be  momentary  or  continuous.  A  momen- 
tary sound  consists  of  a  single  pulse  produced  by  a  single 
and  sudden  blow.  A  continuous  sound  consists  of  a 
rapid  succession  of  pulses.  The  ear  is  so  constructed 
that  its  vibrations  disappear  very  rapidly  but  the  disap- 
pearance is  not  instantaneous.  If  the  motion  imparted 


NATURE   OF  SOUND.  375 

to  the  auditory  nerve  by  each  individual  pulse  con- 
tinue until  the  arrival  of  its  successor,  the  sound 
will  be  continuous. 

(a.)  Momentary  sounds  may  be  produced  by  pounding  with  a 
hammer,  stamping  with  the  foot,  clapping  the  hands  or  drawing  a 
stick  slowly  along  the  pickets  of  a  fence.  Continuous  sounds  may 
be  produced  by  sawing  boards  or  filing  saws.  They  constitute  the 
rattling  of  wheels  over  a  stony  pavement,  the  roar  of  waves  or  the 
crackling  of  a  large  fire. 

491.  Noise  and  Music.— The  sensation  produced 
by  a  series  of  blows  coming  at  irregular  intervals,  is 
unpleasant  and  the  sound  is  called  a  noise.     But  when 
the  air  waves  come  with  sufficient  rapidity  to  render  the 
sound  continuous  and  with  perfect  regularity,  the  sensa- 
tion is  pleasant  and  the  sound  is  said  to   be  musical. 
To  secure  this  pleasing  smoothness  of  music,   the 
sounding  body  must  vibrate  with  the  unerring  reg- 
ularity of  the  pendulum,  but  impart  much  sharper 
and  quicker    shocks    to    the    air.      Every    musical 
sound  has  a  well-defined  period  and  wave  length. 

492.  Elements  of  Musical  Sounds.— Musical  sounds  or 
tones  have  three  elements — intensity  or  loudness,  pitch,  and  timbre 
or  quality.     The  first  two  of  these  we  shall  consider  at  once,  the 
third,  a  little  further  on. 

493.  Intensity  and  Amplitude. — Intensity  or 
loudness  of  sound  depends  upon  the  amplitude  of 
vibration.     The  greater  the  amplitude, '  the  louder  the 
sound. 

(a.)  If  the  middle  of  a  tightly-stretched  cord  or  wire,  as  a  guitar 
string,  be  drawn  aside  from  its  position  of  rest  and  then  set  free,  it- 
will  vibrate  to  and  fro  across  its  place  of  rest,  striking  the  air  and 
sending  sound  waves  to  the  ear.  If  the  middle  of  the  string  be 
drawn  aside  to  a  greater  distance  and  then  set  free,  the  swing  to 
and  fro  will  be  increased,  harder  blows  will  be  struck  upon  the  air. 


376 


NATURE  OF  SOUND. 


and  tlie  air  particles  will  move  forward  and  backward  through  « 
greater  distance.  In  other  words,  the  amplitude  of  vibration  has 
been  increased.  But  this  change  in  the  aerial  wave  produces  a 
change  in  the  sensation.  We  still  recognize  the  pitch  to  be  the 
same  as  before  ;  the  tone  is  neither  higher  nor  lower.  We  even 
recognize  it  still  as  being  produced  by  a  guitar  string.  The  only 
Ufference  is  that  the  sensation  is  more  intense  ;  we  say  that  the 
is  louder. 


494.  Intensity  and  Distance.  —  The  intensity 
of  sound  varies  inversely  as  the  square  of  the  dis- 
tance from  the  sounding  body.  Hence,  the  distance 
to  which  a  sound  may  be  heard  depends  upon  its  intensity. 


"  !'    j-  :"'  -T       "'    !;:  .iMiiM.K'jiii  ||, 


FIG.  259. 

495.  Acoustic  Tubes. — If  the  sound  wave  be  not 
allowed  to  expand  as  a  spherical  shell,  the  energy  of  the 
wave  cannot  be  diffused.  This  means  that  its  intensity 
will  be  maintained.  In  acoustic  tubes  (Fig.  217)  this 
diffusion  is  prevented ;  the  waves  are  propagated  in 


NATURE   OF  SOUND.  377 

only  one  direction.  In  this  way,  sound  may  be  trans- 
mitted to  great  distances  without  considerable  loss  of 
intensity.  (See  First  Principles,  Exp.  149.) 

496.  Pitch. — The  second  element  of  a  musical  sound 
!.s  pitch,  by  which  we  mean  the  quality  that  constitutes 
the  difference  between  a  low  or  grave  tone  and  a  high 
tone.     All  persons  are  more  or  less  able   to  recognize 
differences  in  pitch.     A  person  who  is  able  to  judge 
accurately  of  the  pitch  of  sounds  is  said  to  have  a  "good 
ear  for  music."     The  pitch  of  a  sound  depends  upon 
the  rapidity  of  vibration  of  the    sounding   body, 
or,  in  other  words,  upon  the  rate  at  which  sound  pulses 
follow  each  other.     The  more  rapid  the  vibrations,  the 
higher  the  tone. 

497.  Experimental  Proof  of  the  Cause  of 
Pitch.  —  That    pitch    depends    upon 

rapidity  of  vibration,  may  be  roughly 

shown  by  drawing  the  finger  nail  across 

the  teeth  of  a  comb,  slowly  the  first  time 

and  rapidly  the  second  time.    It  may  be 

shown  more  satisfactorily  by  means  of 

Savart's  wheel,  shown  in  Fig.  260.    This 

consists  of  a  heavy  metal  ratchet-wheel, 

supported  on  an  iron  frame  and  pedestal.     The  wheel  may 

be  set  in  rapid  revolution  by  a  cord  wound  around  the  axis. 

By  holding  a  card  against  the  teeth,  when  in  rapid  motion, 

a  shrill  tone  will  be  produced,  gradually  falling  in  pitch  as 

the  speed  is  lessened. 

(a.)  If  the  sounding  body  and  the  listening  ear  approach  each 
other,  the  sound  waves  will  beat  upon  the  ear  with  greater  rapidity. 
This  is  equivalent  to  increasing  the  rapidity  of  vibration  of  the 


378  NATURE  OF  SOUND. 

sounding  body.  The  opposite  holds  true  when  the  sounding  body 
and  the  ear  recede  from  each  other.  This  explains  why  the  pitch 
of  the  whistle  of  a  railway  locomotive  is  perceptibly  higher  when 
the  train  is  rapidly  approaching  the  observer,  than  when  it  is  rapidly 
moving  away  from  him. 

498.  Relation  between  Pitch  and  Period.— 

Rate  of  vibration  and  period  are  reciprocals.  If  the 
rate  of  vibration  be  256  per  second,  the  period  is  yj¥  01  a 
second.  The  period  may,  therefore,  be  used  to  measure 
the  pitch ;  the  greater  the  period,  the  lower  the  pitch. 

499.  Relation    between   Pitch   and  Wave 
Length. — Since,  in  a  given  medium,  all  sounds  travel 
with  the  same  velocity,  the  rate  of  vibration  determines 
the  wave  length.    If  the  sounding  body  vibrate  224  times 
per  second,  224  waves  will  be  started  each  second.     If  the 
velocity  of  the  sound  be  1120  feet,  the  total  length  of  these 
224  waves  must  be  1120  feet,  or  the  length  of  each  wave 
must  be  five  feet.    If  another  body  vibrate  twice  as  fast, 
it  will  crowd  twice  as  many  waves  into  the  1120  feet;  each 
wave  will  be  only  two  and  a  half  feet  long.    Thus  wave 
length  may  be  used  to  measure  the  pitch — the  greater  the 
wave  length,  the  lower  the  pitch. 

500.  Refraction  of  Sound. — We  have  a  clear 
idea  of  sound  waves  advancing  as  concentric,  spherical 
shells,  but  we  are  far  more  familiar  with  the  idea  of  sound 
advancing  in  definite  straight  lines.     This  idea  is  also  cor- 
rect, the  lines  being  radii  of  the  sphere.    We  may  thus 
speak  of  lines  or  "rays"  of  sound,  meaning  thereby  the 
direction  in  which  the   sonorous   pulses  are   propagated. 
The  ray  is  necessarily  perpendicular  to  the  wave.    When 
the  noise  of  the  street  is  heard  by  a  person  in  a  closed  room, 
the  sound  must  have  passed  from  the  air  without  to  the 


NATURE   OF  SOUND.  379 

solid  matter  of  the  walls,  and  from  this  to  the  air  within. 
When  sound  thus  passes  obliquely  from  one  medium  to 
another,  the  rays  are  bent.  This  bending  of  a  sound 
ray  is  called  refraction  of  sound. 

5O1.  A  Sound  Focus. — Ordinarily,  sound  rays  are 
divergent.  The  sound  is  therefore  continually  diminishing 
in  intensity.  By  means  of  their  refrangibility,  they  may 
be  made  convergent.  If  the  divergent  rays  strike  the  side 
of  a  sack  shaped  like  a  double  convex  lens,  made  of  two 
Sims  of  collodion,  or  very  thin  India  rubber,  and  filled 
with  carbonic  acid  gas  (C02),  their  divergence  will  be  di- 
minished ;  they  may  thus  be  made  parallel,  or  even  con- 
vergent, after  passing  through  the  sack.  At  the  point 
where  these  rays  converge  their  total  energy  will  be  con- 
centrated, and  the  intensity  of  the  sound  be  thus  increased, 
The  point  where  the  refracted  rays  intersect  is  called  the 
focus  of  the  lens.  The  laws  of  refracted  sound  are  the 
same  as  those  of  refracted  light,  to  be  studied  further  on. 

(a.)  If  a  watch  be  hung  near  such  a  refractor,  its  ticking  may  be 
heard  by  placing  the  ear  at  the  focus  on  the  other  side  of  the  sack  ; 
when  the  sack  is  re- 
moved, the  ticking  is 
no  longer  audible.  A 
few  trials  will  enable 
the  experimenter  to 
determine  the  proper 
positions  for  the  watch, 
the  lens  and  the  ear. 
The  refraction  directs 
to  the  ear  all  the  en 

ergy  exerted  upon  the  pIG<  26l 

anterior  surface  of  the 

sack.  This  energy  is  sufficient  to  excite  the  sensation  of  hearing. 
A  little  reflection  will  show  that  when  the  sack  is  removed,  the 
energy  exerted  upon  the  smaller  surface  of  the  tympanum  at  the 


380  NATURE  OF  SOUND. 

greater  distance  is  very  much  diminished.  This  lesser  energy  is 
unable  to  excite  the  auditory  nerve  to  action,  and  the  ticking  of  the 
watch  is  unheard. 

502.  Reflection  of  Sound. — When  a  sound  ray 
strikes  an  obstacle,  it  is  reflected  in  obedience  to  the  prin- 
ciple given  in  §  97.     This  fact  is  turned  to  account  in  the 
case  of  "conjugate  reflectors"  of  sound.    Fig.  262  repre- 
sents the  section  of  two  parabolic  reflectors  mn  and  op. 
It  is  a  peculiarity  of  such  reflect- 
ors that  rays  starting  from  the 

focus,  as  F,  will  be  reflected  as 
parallel  rays,  and  that  parallel  rays 
falling  upon  such  a  reflector  will 

converge    at    the    focus,  as    F' .    \L 

Hence,  two  such  reflectors  may       ^^ 
be  placed  in  such  a  position  that  FJG 

sound  waves  starting  from  one 

focus  shall,  after  two  reflections,  be  converged  at  the  other 
focus.  Two  reflectors  so  placed  are  said  to  be  con- 
jugate to  each  other.  This  principle  underlies  the 
phenomena  of  whispering  galleries. 

(a.)  "  The  great  dome  of  St.  Paul's  Cathedral  in  London  is  so  con- 
structed that  two  persons  at  opposite  points  of  the  internal  gallery, 
placed  in  the  drum  of  the  dome,  can  talk  together  in  a  mere  whisper. 
The  sound  is  transmitted  from  one  to  the  other  by  successive  reflec- 
tions along  the  course  of  the  dome."  A  similar  phenomenon  is 
observable  in  the  dome  of  the  Capitol  at  Washington. 

503.  Experiment. — At  the  focus  of  a  curved  re- 
flector, place  a  watch  or  other  suitable  sounding  body. 
Directly  facing  it,  but  at  a  distance  so  great  that   the 
ticking  is  unheard,  place  a  similar  reflector.    When  the 
ear  is  placed  at  the  focus  of  the  second  mirror,  as  shown  in 
Fig.  263,  the  ticking  is  plainly  heard. 


NATURE  OF  SOUND. 


381 


FIG.  263. 

(a.)  In  the  experiment  above  described,  it  is  plain  that  many  of 
the  rays  reflected  by  the  first  mirror  are  intercepted  before  they 
reach  the  second  mirror.  This  may  be  remedied,  in  part,  by  the 
use  of  an  ear-trumpet,  the  larger  end  being  held  at  the  focus  of  the 
second  reflector.  The  ear-trumpet  may  be  a  glass  funnel,  with  a 
piece  of  rubber  tubing  leading  from  its  smaller  end  to  the  ear.  The 
experiment  may  be  modified  by  using  a  single  reflector,  the  watch 
being  placed  a  little  further  from  the  reflector.  The  proper  positions 
for  the  watch  and  the  funnel  are  easily  determined  by  experiment. 
They  are  conjugate  foci. 

5O4.  Echo. —  When  a  sound,  after  reflection,  is 
audible,  it  is  called  an  echo.  The  distinctness  with 
which  it  is  heard  depends  upon  the  distance  of  the  ear 
from  the  reflecting  surface.  A  very  quick,  sharp  sound 
may  produce  an  echo  even  when  the  reflecting  surface  is 
not  more  than  fifty  or  sixty  feet  away,  but  for  articulate 
sounds  a  greater  distance  is  necessary. 

(a.}  Few,  if  any,  persons  can  pronounce  distinctly  more  than 
about  five  syllables  in  a  second.  At  the  ordinary  temperature, 
sound  travels  about  1120  feet  per  second.  In  a  fifth  of  that  time 
it  would  travel  about  224  feet.  If,  therefore,  the  reflecting  surface 
be  112  feet  distant,  the  articulate  sound  will  go  and  return  before 
the  next  syllable  is  pronounced.  The  two  sounds  will  not  inter- 
fere, and  the  echo  will  be  distinctly  heard.  If  the  reflecting  sur- 
face be  less  than  this  distance,  the  reflected  sound  will  return  before 


382  KATURE  Of  SOUND. 

the  articulation  is  complete  and  confusedly  blend  with  it.  If  th« 
reflector  be  224  feet  distant,  there  will  be  time  to  pronounce  two 
syllables  before  the  reflected  wave  returns.  The  echo  of  both 
syllables  may  then  be  heard  ;  and  so  on.  The  echo  may  be  heard 
sometimes  when  the  direct  sound  cannot  be  heard. 

(&.)  Suppose  the  speaker  to  stand  1120  feet  from  the  reflecting 
substance.  If  then  he  speak  ten  syllables  in  two  seconds,  the  echo 
of  the  first  will  return  just  as  the  last  is  spoken  ;  the  echo  of  each 
syllable  will  be  distinct.  But  if  he  continues  to  speak,  the  direct 
and  the  reflected  sounds  will  become  blended  and  confused.  The 
reflecting  surface  should  be  a  large,  vertical  wall,  or  similar  object, 
as  a  huge  rock. 

(c.)  When  two  opposite  surfaces,  as  parallel  walls,  successively 
reflect  the  sound,  multiple  echoes  are  heard.  Sometimes  an  echo  is 
thus  repeated  20  or  30  times. 

EXERCISES. 

1.  If  18  seconds  intervene  between  the  flash  and  report  of  a  gun, 
what  is  its  distance,  the  temperature  being  82°  F.? 

2.  What  will  be  the  length  of  the  sound  waves  propagated  through 
air  at  a  temperature  of  15°  C.  by  a  tuning-fork  that  vibrates  224 
times  per  second  ? 

3.  State  clearly  the  difference  between  a  transverse  and  a  longi 
tudinal  wave. 

4.  Determine  the  temperature  of  the  air  when  the  velocity  of 
sound  is  1150  feet  per  second. 

5.  If  A  is  50  m.  from  a  bell,  and  B  is  70  m.  from  it,  how  will  the 
loudness  of  the  sound  as  heard  by  B  compare  with  the  loudness  as 
heard  by  A  ? 

6.  A  shot  is  fired  before  a  cliff,  and  the  echo  heard  in  six  seconds. 
The  temperature  being  15°  C.  find  the  distance  of  the  cliff. 

7.  A   certain  musical  instrument   makes    1100  vibrations    per 
second.     Under  what  conditions  will  the  sound  waves  be  each  a  foot 
long? 

8.  How  many  vibrations  per  second  are  necessary  for  the  forma- 
tion of  sound  waves  four  feet  long,  the  velocity  of  sound  being 
1120  feet  ?    What  will  be  the  temperature  at  the  time  of  the  experi- 
ment? 

9.  Taking  the  velocity  of  sound  as  332  m.,  find  the  length  of  a 
wave  if  there  are  830  vibrations  per  second. 

10.  The  waves  produced  by  a  man's  voice  in  common  conversation 
are  from  eight  to  twelve  feet  long.     If  the  velocity  of  sound  be 


COMPOSITION  OF  SOVND    WAVES. 


1128   feet,  find  the  corresponding  numbers  of  vibrations  of  vocal 
chords. 

11.  A  person  stands  before  a  cliflf  and  claps  his  hands.     In  f  of  a 
second  he  hears  the  echo.     How  far  distant  was  the  cliff? 


Recapitulation. — To  be  amplified  by  the  pupil  for 
review. 

DEFINITION    AND   CAUSE. 


SOUND. 


WAVES. 


MEDIA. 


VELOCITY 


MOMENTARY. 


CONTINUOUS.  " 


UNDULATIONS. 

MODE  OF  PROPAGATION. 

PERIOD  AND  LENGTH. 

AMPLITUDE. 

(  CONDENSATION. 
PARTS..  J 

(  RAREFACTION. 

{AT  FREEZING  TEMPERATURE.    . 
AT  OTHER  TEMPERATURES. 
IN  OTHER  MEDIA. 


NOISY. 


MUSICAL. 


(  Cause. 

LOUDNESS.  •< 

(  Acoustic  Tubes 
PITCH Cause. 

RELATION  BETWEEN  PITCH 
AND  PERIOD. 


QUALITY  OR  TIMBRE. 

REFRACTION  AND  ACOUSTIC  FOCI. 

f  LAW. 

REFLECTION..  \  WHISPERING  GALLERIES. 
1  ECHOES. 


384 


THE  TELEPHONE. 


s 


ECTfON  IK 


THE  TELEPHONE   AND    PHONOGRAPH.— COMPOSI- 
TION   AND  ANALYSIS  OF   SOUNDS. 

Note. — Before  beginning  the  study  of  the  telephone,  the  pupil 
should  carefully  review  §§  468,  469. 

5O5.  The  Telephone. — This  instrument  is  repre- 
sented in  section  by  Fig.  264.      A   is  a  permanent  bar 

magnet,  around 
one  end  of  which 
is  wound  a  coil, 
/>,  of  fine  copper 
wire  carefully 
insulated.  The 
ends  of  this 
coiled  wire  are 


PIG.  264. 


attached  to  the  larger  wires,  (7(7,  which  communicate  with 
the  binding  posts,  DD.  In  front  of  the  magnet  and  coil 
is  the  soft  iron  diaphragm,  E,  which  corresponds  to  the 
disc,  0,  of  Fig.  249.  The  distance  between  E  and  the 
end  of  A  is  delicately  adjusted  by  the  screw,  S.  In  front 
of  the  diaphragm,  is  a  wooden  mouth-piece  with  a  hole 
about  the  size  of  a  dime,  at  the  middle  of  the  diaphragm 
and  opposite  the  end  of  the  magnet.  The  outer  case  is 
made  of  wood  or  of  hard  rubber.  The  external  appearance 
of  the  complete  instrument  is  represented  by  Fig.  265. 


THE   TELEPHONE.  385 

The  binding  posts  of  one  instrument  being  connected  by 
wires  with  the  binding  posts  of  another  at  a  distance,  con- 
versation may  be  carried  on  between 
them. 

5O6.  Action  of  the  Tele- 
phone.— When  the  mouth-piece  is 
brought  before  the  lips  of  a  person 
who  is  talking,  air  waves  beat  upon 
the  diaphragm  and  cause  it  to  vibrate. 
The  nature  of  these  vibrations  depends 
upon  the  loudness,  pitch  and  timbre 
of  the  sounds  uttered.  Each  vibration 
of  the  diaphragm  induces  an  electric 
current  in  the  wire  of  B.  These  cur- 
rents are  transmitted  to  the  coil  of  the 
connected  telephone,  at  a  distance  of, 
perhaps,  several  miles,  and  there  produce,  in  the  diaphragm 
of  the  instrument,  vibrations  exactly  like  the  original 
vibrations  produced  by  the  voice  of  the  speaker.  These 
vibrations  of  the  second  diaphragm  send  out  new  air 
waves  that  are  very  faithful  counterparts  of  the  original 
air  waves  that  fell  upon  the  first  diaphragm.  The  two 
sets  of  air  waves  being  alike,  the  resulting  sensations  pro- 
duced in  the  hearers  are  alike.  Not  only  different  words 
but  also  different  voices  may  be  recognized.  The  arrange- 
ment being  the  same  at  both  stations,  the  apparatus  works 
in  either  direction.  No  battery  is  necessary  with  this 
arrangement.  (See  Appendix  0.) 

(a.)  The  reproduced  sound  is  somewhat  feeble  but  remarkably 
clear  and  distinct.  The  second  telephone  should  be  held  close  to 
the  ear  of  the  listener.  Sometimes  there  are,  in  the  same  circuit, 


386 


THE   TELEPHONE. 


two  or  more  instruments  at  each  station,  so  that  each  operator  maj 
hold  one  to  the  ear  and  the  other  to  the  month  ;  or  the  listener  may 
place  one  at  each  ear.  When  the  stations  are  a  considerable  dis 
tance  apart,  one  binding  post  of  each  instrument  may  be  connected 
with  the  earth,  as  in  the  case  of  the  telegraph  (§  444). 

(b.)  It  is  to  be  distinctly  noticed  that  the  sound  waves  are  not 
transmitted  from  one  station  to  the  other.  "  The  air  waves  are 
spent  in  producing  mechanical  vibrations  of  the  metal ;  these  create 
magnetic  disturbances  that  excite  electrical  acuon  in  the  wire, 
and  this  again  gives  rise  to  magnetic  changes  that  are  still  further 
converted  into  the  tremors  of  the  distant  diaphragm,  and  these 
finally  reappear  as  new  trains  of  air  waves  that  affect  the  listener." 


TO  THf  caoufjo 


FIG.  266. 

5O7.  The  Transmitter.— In  practice,  a  transmit- 
ter, shown  at  C  in  Fig.  266,  is  generally  used.  The  vibra- 
tions of  the  diaphragm  of  C,  when  acted  upon  by  sound 
waves,  produce  a  varying  pressure  upon  a  carbon  button 
placed  in  the  circuit  of  a  galvanic  battery,  />.  This  vary- 


THE  PHONOGRAPH.  38? 

ing  pressure  results  in  a  varying  resistance  to  the  passage 
of  the  current  through  the  button  and,  consequently,  in 
variations  in  the  current  itself.  This  varying  current, 
passing  through  the  primary  circuit  of  a  small  induction 
coil  in  the  box,  C,  induces  a  current  in  the  secondary  cir- 
cuit thereof.  This  current,  thus  induced,  flows  over  the 
telephone  wires  and,  at  the  other  station,  passes  through  a 
telephone  like  that  shown  at  B,  which  is  held  close  to 
the  ear  of  the  listener.  The  message  is  transmitted  by  C 
at  one  station  and  received  by  B,  of  a  similar  instrument, 
at  the  other  station. 

At  each  station  is  placed  an  electric  bell,  A,  which  may 
be  rung  from  the  other  station,  for  the  purpose  of  at- 
tracting attention.  When  the  stations  are  a  considerable 
distance  apart,  one  binding  post  of  each  instrument 
may  be  connected  with  the  earth,  as  in  the  case  of  the 
telegraph. 

(a.)  In  most  of  our  cities,  the  telephones  are  connected  by  wire 
with  a  central  station,  called  a  telephone  exchange.  The  "  Ex- 
change "  may  thus  be  connected  with  the  houses  of  hundreds  of 
patrons  in  all  parts  of  the  city  or  even  in  different  cities.  Upon  re- 
quest by  telephone,  the  attendant  at  the  central  station  connects 
the  line  from  any  instrument  with  that  running  to  any  other  instru- 
ment. Thus,  each  subscriber  may  communicate  directly  with  any 
other  subscriber  to  the  exchange. 

5O8.  The  Phonograph. — This  is  an  instrument 
for  recording  sounds  and  reproducing  them  after  any 
length  of  time.  (See  Appendix  P.) 

(a.)  The  receiving  apparatus  consists  of  a  mouth-piece  and 
vibrating  disc  like  those  of  the  telephone.  At  the  back  of  the 
disc  is  a  short  needle  or  style  for  recording  the  vibrations  upon  a 
sheet  of  tin-foil  moving  under  it.  This  tin-foil  is  placed  upon  a  metal 
cylinder  about  a  foot  (30  cm.)  long.  The  cylinder  has  a  spiral 


THE  PHOXOGHAPB. 


groove  upon  its  curved  surface  and  a  similar  thread  upon  its  axis, 
which  turns  in  a  fixed  nut.  As  the  cylinder  is  turned  by  a  crank, 
the  threads  upon  the  axis  give  the  cylinder  a  lengthwise  motion. 
The  style  is  placed  in  position  over  one  of  the  tin-foil  covered 
grooves  of  the  cylinder.  As  the  cylinder  revolves,  a  projection  in 
front  of  the  style  crowds  the  foil  down  into  the  groove.  The  needle 
follows  in  the  channel  thus  made  and,  as  it  vibrates,  records  a  suc- 
cession of  dots  in  the  tin-foil.  These  dots  constitute  the  record.  To 
the  naked  eye  they  look  alike,  but  the  microscope  reveals  differences 
corresponding  to  pitch,  loudnees,  and  timbre. 

(b.)  To  reproduce  the  sound,  the  style  is  lifted  from  the  foil,  the 
cylinder  turned  back  to  its  starting  point,  the  style  placed  in  the 
beginning  of  the  groove  and  the  crank  turned.  The  style  passes 
through  the  channel  and  drops  into  the  first  indentation  ;  the  disc 
follows  it.  The  style  rises  and  drops  into  each  of  the  succeeding 
indentations,  the  disc  following  its  every  motion  with  a  vibration. 
The  original  vibrations  made  the  dots ;  the  dots  are  now  making 
similar  vibrations.  Sound  waves  made  the  original  vibrations ;  now 
the  reproduced  vibrations  create  similar  sound  waves.  The  repro- 
duced sounds  are  a  little  muffled  but  remarkably  distinct,  each  of  the 
three  qualities  (§  492)  being  recognizable.  The  principle  may  be 
applied  to  any  implement  or  toy  that  makes  a  sound  as  well  as  to 
the  voice.  Perfectly  simple  ;  equally  wonderful. 

Experiment  I. — The  effect  of  repeated  impulses,  each  feeble 
but  acting  at  the  right  instant,  may  be  forcibly  illustrated  as  follows : 
Support  a  heavy  weight,  as  a  bucket  of  coal,  by  a  long  string  or 
wire.  To  the  handle  of  a  bucket,  fasten  a  fine  cotton  thread.  By 
repeated  pulls  upon  the  thread,  each  pull,  after  the  first  one,  being 
given  just  as  the  pendulum  is  beginning  to  swing  toward  you 
from  the  effect  of  the  previous  pull,  the  weight  may  be  made  to 
swing  through  a  large  arc,  while  a  single  pull  out  of  time  will 
snap  the  thread.  A  little  practice  will  enable  you  to  perform  the 
experiment  neatly. 

Experiment  2. — Vary  the  last  experiment  by  setting  the  pendu- 
lum in  motion  by  well-timed  puffs  of  air  from  the  mouth  or  from  a 
hand  bellows.  The  same  principle  is  illustrated  in  the  action  of  the 
spring  board,  familiar  to  most  boys,  who  know  that  the  desired 
effect  can  be  secured  only  by  "  keeping  time."  Soldiers  are  often 
ordered  to  "break  step"  in  crossing  a  bridge,  lest  the  accumulated 
energy  of  many  footfalls  in  unison  break  the  bridge. 

Experiment    3. — Suspend  several  pendulums  from  a  frame  as 


SYMPATHETIC    VIBRATIONS. 


389 


d  c  b 


shown  in  Fig.  267.     Make  two  of  equal  length  so  that  they  will 
vibrate  at  the  same  rate.    Be  sure  that  they  will  thus  vibrate.     The 
other  pendulums  are  to  be  of  different  lengths.     Set  a  in  vibration. 
The  swinging  of  a  will  produce  slight  vibra- 
tions in  the  frame  which  will,  in  turn,  trans- 
mit them  to   the   other  pendulums.     As  the 
successive  impulses  thus  imparted  by  a  keep 
time  with  the  vibrations  of  &,  this  energy  ac- 
cumulates in  b,  which  is  soon  set  in  perceptible 
vibration.    As  these  impulses  do  not  keep  time 
with  the  vibrations  of  the  other  pendulums, 
there  can  be  no  such  accumulation  of  energy 
in  them,  for  many  of  the  impulses  will  act  in 
opposition  to  the  motions  produced  by  previous 
impulses  and  tend  to  destroy  them. 

Experiment  4. — Tune  to  unison  two  strings 
upon  the  same  sonometer  (Fig.  268).  Upon 
one  string,  place  two  or  three  paper  riders. 
With  a  violin  bow,  set  the  other  string-  in  vi- 
bration. The  sympathetic  vibrations  thus 
produced  will  be  shown  by  the  dismounting 
of  the  riders,  whether  the  vibrations  be  audible  JTIG  267 

or  not.      Change  the  tension  of  one  of  the 

strings,  thus  destroying  the  unison.      Repeat  the  experiment  and 
notice  that  the  sympathetic  vibrations  are  not  produced.     See  App.  Q. 


FIG.  268. 

Experiment  5.  —  Place,  several  feet  apart,  two  tuning-forks 
mounted  upon  resonant  cases.  The  forks  should  have  the  same 
tone  and  the  cases  should  rest  upon  pieces  of  rubber  tubing  to  pre- 
vent thie  transferrence  of  vibratory  motion  to  and  through  the  table, 


390  SYMPATHETIC    VIBRATIONS. 

Sound  the  first  fork  by  rapidly  separating  the  two  prongs  with  a 
rod  or  by  rubbing  it  with  a  violin  bow.  Notice  the  pitch.  At  the 
end  of  a  second  or  two,  touch  the  prongs  to 
stop  their  motion  and  sound.  It  will  be  found 
that  the  second  fork  has  been  set  in  motion  by 
the  repeated  blows  of  the  air  and  is  giving 
forth  a  sound  of  the  same  pitch  as  that  orig- 
inally produced  by  the  first  fork.  Fasten, 
by  means  of  wax,  a  3-cent  silver  piece  or 
other  small  weight  to  one  of  the  prongs  of 
the  second  fork.  An  attempt  to  repeat  the 
FIG.  269.  experiment  will  fail.  When  the  two  forks  are 

in  unison,  their  periods  are  the  same.     The 

second  and  subsequent  pulses  sent  out  by  the  first  fork  strike  the 
second  fork,  already  vibrating  from  the  effect  of  the  first  pulse,  in 
the  same  phase  of  vibration  and  thus  each  adds  its  effect  to  that 
of  all  its  predecessors.  If  the  forks  be  not  in  unison,  their  periods 
will  be  different  and  but  few  of  the  successive  pulses  can  strike  the 
second  fork  in  the  same  phase  of  vibration  ;  the  greater  number 
will  strike  it  at  the  wrong  instant. 

5O9.  Sympathetic  Vibrations. — The  string  of  a 
violin  may  be  made  to  vibrate  audibly  by  sounding  near 
it  a  tuning-fork  of  the  same  tone.  By  prolonging  a  vocal 
tone  near  a  piano,  one  of  the  wires  seems  to  take  up  the 
note  and  give  it  back  of  its  own  accord.  If  the  tone  be 
changed,  another  wire  will  give  it  back.  In  each  case, 
that  wire  is  excited  to  audible  action,  which  is  able  to 
vibrate  at  the  same  rate  as  do  the  sonorous  waves  that  set 
it  in  motion.  Thus  the  vibrations  of  the  strings  may  pro- 
duce sonorous  waves  and  the  waves,  in  turn,  may  produce 
vibrations  in  another  string.  The  most  important  feature 
of  the  phenomenon  is  that  the  string  absorbs  only  the 
particular  kind  of  vibration  that  it  is  capable  of 
producing. 

Experiment  6.— Strike  a  tuning-fork  held  in  the  hand.  Notice 
the  feeble  sound.  Strike  the  fork  again  and  place  the  end  of  tht? 


SOUNDING  BOARDS.  391 

handle  upon  a  table.     The  loudness  of  the  sound  heard  is  remark 
ably  increased. 

Experiment  7. — Strike  the  fork  and  hold  it  near  the  ear,  count- 
ing the  number  of  seconds  that  you  can  hear  it.  Strike  the  fork 
again  with  equal  force ;  place  the  end  of  the  handle  on  the  table 
and  count  the  number  of  seconds  that  you  can  hear  it. 

51O.  Sounding-Boards.  —  In  the  case  of  the 
sonometer,  piano,  violin,  guitar,  etc.,  the  sound  is  due 
more  to  the  vibrations  of  the  resonant  bodies  that  carry 
the  strings  than  to  the  vibrations  of  the  strings  them- 
selves. The  strings  are  too  thin  to  impart  enough  motion 
to  the  air  to  be  sensible  at  any  considerable  distance  ;  but 
as  they  vibrate,  their  tremors  are  carried  by  the  bridges  to 
the  material  of  the  sounding  apparatus  with  which  they 
are  connected.  These  larger  surfaces  throw  larger  masses 
of  air  into  vibration  and  thus  greatly  intensify  the  sound. 
It  necessarily  follows  that  the  energy  of  the  vibrating 
body  is  sooner  exhausted;  the  sounds  are  of  shorter 
duration. 

(#.)  This  sounding  apparatus  usually  consists  of  thin  pieces  of 
wood  that  are  capable  of  vibrating  in  any  period  within  certain 
limits.  The  vibrations  of  these  large  surfaces  and  of  the  enclosed 
air  produce  the  sonorous  vibrations.  The  excellence  of  a  Cremona 
violin  does  not  lie  in  the  strings,  which  may  have  to  be  replaced 
daily.  The  strings  are  valuable  to  determine  the  rate  of  vibration 
that  shall  be  produced  (§  519).  The  excellence  of  the  instrument 
depends  upon  the  sonorous  character  of  the  wood,  which  seems  to 
improve  with  age  and  use. 

(6.)  Similar  remarks  apply  to  the  tuning-fork.  Hence,  for  class 
or  lecture  experiments,  tuning-forks  should  be  mounted  as  shown 
in  Fig.  269. 

Experiment  8. — Support  horizontally,  between  two  fixed  sup- 
ports, a  soft  cotton  rope  a  few  yards  in  length.  With  a  stick, 
strike  the  rope  near  one  end  a  blow  from  below  and  a  crest  will 
be  formed  as  shown  in  Fig.  270.  Vary  the  tension  of  the  rope,  if 


392  COINCIDENT  SOUND    WAVES. 

necessary,  until  the  crest  is  easily  seen.     Notice  that  the  crest,  c, 
travels  from  A  to  B  where  it  is  reflected  back  to  A  as  a  trough,  t 


B 


FIG.  270. 

By  striking  the  rope  from  above,  a  trough  may  be  started  which 
will  be  reflected  as  a  crest. 

Experiment  9.— From  A,  start  a  trough.  At  the  moment  of  its 
reflection  as  a  crest  at  B,  start  a  crest  at  A  as  shown  in  Fig.  271. 
The  two  crests  will  meet  near  the  middle  of  the  rope.  The  crest 
at  the  point  and  moment  of  meeting  results  from  two  forces  acting 


FIG.  271. 

in  the  same  direction,  consequently  it  will  be  greater  than  either 
of  the  component  crests. 

511.  Coincident   Waves. — In  the  case  of  water 
waves,  when  crest  coincides  with  crest  the  water  reaches  a 
greater  height.     So. with  sound  waves,  when  condensation 
coincides  with  condensation,  this  part  of  the  wave  will  be 
more  condensed;  when  rarefaction  coincides  with  rarefac- 
tion, this  part  of  the  wave  will  be  more  rarefied.     This 
increased  difference  of  density  in    the   two   parts  of  the 
wave   means   increased   loudness  of  the   sound,   because 
there  is  an  increased  amplitude  of  vibration  for  the  par- 
ticles constituting  the  wave. 

512.  Reinforcement  of  Sound. — This  increased 
intensity  may  result  from  the  blending  of  two  or  more 
series  of  similar  waves  in  like  phases,  or  from  the  union  of 


RESONANCE. 


393 


direct  and  reflected  waves  in  like  phases.  Under  such 
circumstances,  one  set  of  waves  is  said  to  reinforce  the 
other.  The  phenomenon  i§  spoken  of  as  a  reinforce- 
ment of  sound. 

Experiment  10. — Hold  a  sounding  tuning-fork  over  the  mouth  of 
a  glass  jar,  18  or  20  inches  -v 

deep ;  a  feeble  sound  is 
heard.  On  carefully  pour- 
ing1 in  water,  we  notice 
that  when  the  liquid 
reaches  a  certain  level, 
the  sound  suddenly  be- 
comes much  louder.  The 
water  has  shortened  the 
air  column  until  it  is  able 
to  vibrate  in  unison  with 
the  fork.  If  more  water 
be  now  poured  in,  the  in- 
tensity of  the  sound  is 
lessened.  If  a  fork  of  dif- 
ferent vibration  be  used, 
the  column  of  air  that 
gives  the  maximum  reso- 
nance will  vary,  the  air 
column  becoming  shorter 
as  the  rate  of  vibration  of 
the  fork  increases.  The 
length  of  the  air  column 
is  one-fourth  the  length  of  the  wave  produced  by  the  fork. 


FIG.  272. 


513.  Resonance. — Resonance  is  a  variety  of  the 
reinforcement  of  sound  due  to  sympathetic  vibrations. 
The  resonant  effects  of  solids  were  shown  in  §  510. 
The  resonance  of  an  air  column  was  well  shown  by  the 
last  experiment. 

(a.)  Fig.  273  represents  Savart's  bell  and  resonator.  The  bell, 
on  being  rubbed  with  the  bow,  produces  a  loud  tone.  The  resonator 
is  a  tube  with  a  movable  bottom.  The  length  of  the  resonant  air 
column  is  changed  by  means  of  this  movable  bottom.  The  point 


394 


RESONANCE. 


at  which  the  reinforcement  of  sound  is  greatest  is  easily  found  by 
trial.     If,  when  the  sound  of  the  bell  has  become  hardly  audible, 

the  tube  be  brought  near, 
the  resonant  effect  is  very 
marked. 


514.  Helmholtz's 
Resonators. — Helm- 
holtz,  the  German 
physicist,  constructed  a 
series  of  resonators, 
each  one  of  which  re- 


FIG.  273. 


sounds  powerfully  to  a  single  tone  of  certain  pitch  or 
wave  length.  They  are  metallic  vessels,  nearly  spherical, 
having  a  large  opening, 
as  at  A  in  Fig.  274, 
for  the  admission  of 
the  sound  waves.  The 
funnel-shaped  projec- 
tion at  B  has  a  small 
opening  and  is  inserted 
in  the  outer  ear  of  the 
observer. 

FIG.  274. 

Experiment    II. — Using 

the  rope  as  described  in  Experiment  8,  start  a  crest  at  A.  At  the 
moment  of  its  reflection  at  B  as  a  trough,  start  a  second  crest  at  A. 
The  trough  and  crest  will  meet  near  the  middle  of  the  rope.  The 


FIG.  275. 

rope  at  this  time  and  place  will  be  urged  upward  by  the  crest  and 
downward  by  the  trough.  The  resultant  effect  of  these  opposing 
forces  will,  of  course,  be  equal  to  their  difference.  If  crest  and 
trough  exert  equal  forces,  the  difference  will  be  zero.  Consequently 


INTERFERENCE   OF  SOUND. 


395 


the  motion  of  the  rope  at  the  meeting  of  crest  and  trough  will  be 
little  or  nothing.  Thus  one  wave  motion  may  be  made  to  destroy  the 
effect  of  another  wave  motion. 

Experiment  12. — Hold  a  vibrating  tuning-fork  near  the  ear  and 
slowly  turn  it  between  the  fingers.  During  a  single  complete  rota- 
tion, four  positions  of  full  sound  and  four  positions  of  perfect  silence 
will  be  found.  When  a  side  of  the  fork  is  parallel  to  the  ear,  the 
sound  is  plainly  audible  ;  when  a  corner  of  a  prong  is  turned  toward 
the  ear,  the  waves  from  one  prong  completely  destroy  the  waves  started 
by  the  other.  The  interference  is  complete. 

Experiment  13. — Over  a  resonant  jar,  as  shown  in  Fig.  272,  slowly 
turn  a  vibrating  tuning-fork.  In  four  positions  of  the  fork  we  have 


FIG. 


loud,  resonant  tones ;  in  four  other  positions  we  have  complete 
interference.  If,  while  the  fork  is  in  one  of  these  positions  of  inter- 
ference, a  pasteboard  tube  be  placed  around  one  of  the  vibrating 
prongs,  a  resonant  tone  is  instantly  heard ;  the  cause  of  the  inter- 
ference has  been  removed.  (Fig.  276.) 


515.  Interference  of  Sound.— If,  while  a  tuning- 
fork  is  vibrating,  a  second  fork  be  set  in  vibration,  the 


396 


INTERFERENCE   OF  SOUND. 


waves  from  the  second  must  traverse  the  air  set  in  motion 
by  the  former.    If  the  waves  from  the  two  forks  be  of 


FIG.  277. 

equal  length,  as  will  be  the  case  when  the  two  forks  have 
the  same  pitch,  and  the  forks  be  any  number  of  whole 
wave  lengths  apart  (Fig.  277),  the  two  sets  of  waves  will 
unite  in  like  phases  (condensation  with  condensation, 
etc.),  and  a  reinforcement  of  sound  will  ensue.  But -if  the 
second  fork  be  placed  an  odd  number  of  half  wave  lengths 
behind  the  other,  the  two  series  of  waves  will  meet  in 
opposite  phases ;  where  the  first  fork  requires  a  condensa- 
tion, the  second  will  require  a  rarefaction.  The  two  sets 
of  waves  will  interfere,  the  one  with  the  other.  If  the 
waves  be  of  equal  intensity,  the  algebraic  sum  of  these 
component  forces  will  be  zero.  The  air  particles,  thus 
acted  upon,  will  remain  at  rest ;  this  means  silence.  In 


FIG.  278. 

Fig.  278,  an  attempt  is  made  to  represent  this  effect  to 
the  eye,  the  uniformity  of  tint  indicating  the  absence  of. 
condensations  and  rarefactions.     Thus,  by  adding  sound 
to  sound,  both  may  be  destroyed.     This  is  the  lead- 


BEATS.  397 

ing  characteristic  property  of  wave  motion.  The 
phenomenon  here  described  is  called  interference 
of  sound. 

(a.)  The  sound  of  a  vibrating  tuning-fork  held  in  the  hand  is 
almost  inaudible.  The  feebleness  results  largely  from  interference. 
As  the  prongs  always  vibrate  in  opposite  directions  at  the  same 
time,  one  demands  a  rarefaction  where  the  other  demands  a  con- 
densation. By  covering  one  vibrating  prong  with  a  pasteboard 
tube,  the  sound  is  more  easily  heard. 

Experiment  14.— In  a  quiet  room,  strike  simultaneously  one  of 
the  lower  white  keys  of  a  piano  and  the  adjoining  black  key.  A 
series  of  palpitations  or  beats  will  be  heard. 

Experiment  15. — Simultaneously  sound  the  two  tuning-forks 
described  in  Experiment  5,  one  being  loaded  as  there  mentioned ; 
the  beats  will  be  very  perceptible.  Replacing  the  3-cent  piece  suc- 
cessively by  a  silver  half-dime  and  a  dime,  the  number  of  beats  will 
be  successively  increased. 

516.  Beats. — If  two  tuning-forks,  A  and  B,  vibrating 
respectively  255  and  256  times  a  second,  be  set  in  vibration 
at  the  same  time,  their  first  waves  will  meet  in  like  phases 
and  the  result  will  be  an  intensity  of  sound  greater  than 
that  of  either.  After  half  a  second,  B  having  gained  half 
a  vibration  upon  A,  the  waves  will  meet  in  opposite  phases 
and  the  sound  will  be  weakened  or  destroyed.  At  the  end 
of  the  second  we  shall  have  another  reinforcement ;  at 
the  middle  of  the  next  second  another  interference.  This 
peculiar  palpitating  effect  is  due  to  a  succession 
of  reinforcements  and  interferences,  and  is  called 
a  beat.  The  number  of  beats  per  second  equals  the  dif- 
ference of  the  two  numbers  of  vibration. 

(a.)  If  two  large  organ  pipes,  having  exactly  the  same  tone,  be 
simultaneously  sounded,  a  low,  loud,  uniform  sound  will  be  pro- 
duced. If  an  aperture  be  made  in  the  upper  part  of  one  of  the 
walls  of  one  of  the  pipes  and  closed  by  a  movable  plate,  the  tone 


398  VIBRATIONS  OF  STRINGS. 

produced  by  the  pipe  may  be  changed  at  will.  The  more  the  aper- 
ture is  opened,  the  higher  the  pitch.  In  this  manner,  digliily  raise 
the  pitch  of  one  of  the  pipes.  If  the  pipes  be  sounded  in  succession, 
even  a  trained  ear  would  probably  fail  to  detect  any  difference.  If 
they  be  sounded  simultaneously,  the  sound  will  be  of  varying  loud- 
ness,  very  marked  jerks  or  palpitations  being  perceptible. 

517.  Practical  Effect  of  Beats.— The  human 
ear  may  recognize  about  38,000  different  sounds.      If  a 
string,  for  example,  vibrating  400  times  per  second  were 
sounded,  and  one  vibrating  401    times  per   second  were 
subsequently  sounded,  the  ear  would  probably  fail  to  detect 
any  difference  between  them.     But  if  they  were  sounded 
simultaneously,  the  presence  of  one  beat  each  second  would 
clearly  indicate  the  difference.     Unaided  by  the  beats,  the 
ear  can  detect  about  one  per  cent,  of  the  38,000  sounds 
lying  within  the  range  of  the  human  ear.      Beats  are, 
therefore,  very  important  to  the  tuner  of  musical  instru- 
ments.    To  bring  two  slightly  different  tones  into  unison, 
he  has  only  to  tune  them  so  that  the  beats  cease. 

518.  Vibrations  of  String's.— The  laws  of  musical  tones 
are  most   conveniently  studied  by  means  of  stringed  instruments. 
In  the  violin,  etc.,  the  strings  are  set  in  vibration  by  bowing  them. 
The  hairs  of  the  bow,  being  rubbed  with  rosin,  adhere  to  the  string 
and  draw  it  aside  until  slipping  takes  place.     In  springing  back, 
the  string  is  quickly  caught  again  by  the  bow  and  the  same  action 
repeated.     In  the  harp  and  guitar,  the  strings  are  plucked  with  the 
finger.      In  the  piano,  the  wires  are  struck  by  little  leather-faced 
hammers  worked  by  the  keys,     The  vibrations  of  the  string,  and 
consequently  the  pitch,  depend  upon  the  string  itself.     The  manner 
of  producing  the  vibrations  has  no  effect  upon  the  pitch. 

519.  Laws  of  the  Vibrations  of  Strings.— 

The  following  are  important  laws  of  musical  strings: 
(1.)  Other  conditions  being  the  same,  the  number  of 


VIBRATIONS  OF  STRINGS.  399 

vibrations  per  second  varies  inversely  as  the  length  of  the 
string. 

(2.)  Other  conditions  being  the  same,  the  number  of 
vibrations  per  second  varies  directly  as  the  square  root  of 
the  stretching  weight,  or  tension. 

(3.)  Other  conditions  being  the  same,  the  number  01 
vibrations  per  second  varies  inversely  as  the  square  root  of 
the  weight  of  the  string  per  linear  unit. 

(a.)  All  of  these  laws  may  be  roughly  illustrated  by  means  of  a 
violin.  The  length  of  the  string  may  be  altered  by  fingering ;  the 
tension  may  be  changed  by  means  of  the  screws  or  keys ;  the  effects 
of  the  third  law  may  be  shown  by  the  aid  of  the  four  strings. 

(&.)  For  the  illustration  of  these  laws,  the  sonometer,  shown  in 
Fig.  279,  is  generally  used.  The  length  of  the  string  is  determined 


FIG.  279. 

by  the  two  fixed  bridges,  or  by  one  of  them  and  the  movable  bridge 
which  may  be  employed  for  changing  the  length  of  the  vibrating  part 
of  the  string ;  the  tension  is  regulated  by  pegs  or  by  weights  that 
may  be  changed  at  pleasure  ;  the  third  law  may  be  verified  by  using 
different  strings  of  known  weights.  Iron  and  platinum  wires  of  the 
same  diameters  are  frequently  used  for  this  purpose.  (Appendix  Q.) 
(c.)  From  these  laws  it  follows,  for  example,  that  a  string  of  half 
the  length,  or  four  times  the  tension,  or  one-fourth  the  weight  of  a 
given  string  will  vibrate  just  twice  as  fast  as  the  given  string,  i.e., 
twice  as  fast  on  account  of  any  one,  of  these  three  variations.  A 
string  of  one-third  the  length,  or  nine  times  the  tension,  or  one 
ninth  the  weight  of  a  given  string,  will  vibrate  three  times  as  fast 
as  the  given  string ;  and  so  on, 


400  THE  MUSICAL   SCALE. 

520.  The   Musical   Scale.— Starting    from   any 
•  arbitrary  tone  or  absolute  pitch,  the  voice  rises  or  falls  in 

a  manner  very  pleasing  to  the  ear,  by  eight  steps  or  inter- 
vals. The  whole  series  of  musical  tones  may  be  divided 
into  octaves,  or  groups  of  eight  tones  each,  the  relation 
between  any  two  members  of  one  group  being  the  same  as 
the  relation  between  the  corresponding  members  of  any 
other  group.  The  eighth  of  the  first  group  becomes  the 
first  of  the  second.  The  intervals  between  the  successive 
tones  are  not  the  same,  as  will  be  seen  from  the  next 
paragraph. 

521.  Relative  Numbers  of  Vibrations. — A 

string  vibrating  half  as  rapidly  as  a  given  string,  will  give 
its  octave  below ;  one  vibrating  twice  as  rapidly,  its  octave 
above.  The  ratio  of  the  number  of  vibrations  correspond- 
ing to  the  interval  of  an  octave  is,  therefore,  1:2.  The 
relative  number  of  vibrations  corresponding  to  the  tones 
that  constitute  the  major  diatonic  scale  (gamut)  are  as 
follows : 


Relative  Names,  -        -        -        1,  2,  3,  4,  5,  6,  7,  8. 

Absolute  Names,               -        -    C,  D,  E,  F,  G,  A,  B,  C. 

Syllables,      -                                 do,  re,  mi,  fa,  sol,  la,  si,  do. 

Relative  Numbers  of  Vibrations,  \,  f ,  £ ,  |,  f ,  f ,  -1/,  2. 

24,  27,  30,  32,  36,  40,  45,  48. 

522.   Absolute   Numbers   of  Vibrations.— 

Knowing  the  number  of  vibrations  that  constitute  the 
tone  called  do,  the  absolute  number  of  vibrations  of  any 
of  the  other  tones  of  the  scale  may  be  obtained  by  multi- 
plying the  number  of  vibrations  of  do  by  the  ratio  between 
it  and  that  of  the  given  tone,  as  shown  above.  Thus,  if  C 


ABSOLUTE  PITCH.  401 

have  256  vibrations  per  second,  G  will  have  256  x  f  =  384 
vibrations  per  second  ;  its  octave  will  have  512 ;  the  fifth 
of  its  octave  will  have  512  x  f  —  768.  If  F  be  given  352 
vibrations,  C  will  have  352  -j-  ^  =  264.  Thus,  knowing  C, 
any  given  tone  may  have  its  number  of  vibrations  deter- 
mined by  multiplying  by  the  proper  ratio. 

523.  Absolute  Pitch. — The  number  of  vibrations 
constituting  the  tone  called  0  is  purely  arbitrary.  The 
assignment  of  256  complete  vibrations  to  middle  G  is  com- 
mon, but  the  practice  of  musicians  is  not  uniform.  A 
certain  tuning-fork  deposited  in  the  Conservatory  of  Music 
at  Paris  is  the  standard  for  France ;  it  assigns  261  vibra- 
tions per  second  to  middle  C.  The  standard  tuning-fork 
adopted  by  English  musicians  and  deposited  with  the 
Society  of  Arts  in  London,  gives  264  vibrations  to  middle 
C.  Multiplying  the  numbers  in  the  last  line  of  §  521  by 
11,  we  shall  have  the  absolute  numbers  of  vibration  for  the 
several  tones  of  the  gamut  corresponding  to  this  standard. 

(a.)  Whatever  be  the  standard  thus  adopted,  an  instrument  will 
be  in  tune  when  the  relative  number  of  vibrations  is  correct.  The 
string  that  produces  the  tone  G  must  always  vibrate  three  times 
while  the  one  producing  C  vibrates  twice,  or  36  times,  while  the 
latter  vibrates  24  times.  While  the  string  yielding  D  vibrates  27 
times,  the  string  yielding  B  must  vibrate  45  times  ;  and  so  on. 

(&.)  Middle  G  is  the  tone  sounded  by  the  key  of  a  piano  at  the  left 
of  the  two  black  keys  near  the  middle  of  the  key-board.  It  is 
designated  by  Ci.  (See  Exp.  16,  p.  404.)  Its  octaves  below  and  above 
are  designated  as  follows : 

CL2,     CLi,     0,     Ci,     C2,     Cs,     G,. 

524:.  Fundamental  Tones  and  Overtones. — 

A  string  may  vibrate  transversely  as  a  whole,  or  as  inde- 
pendent segments.  Such  segments  will  be  aliquot  parts 
of  the  whole  string  and  separated  from  each  other  by  points 


402  FUNDAMENTALS  AND  HARMONICS. 

of  no  motion,  called  nodes  or  nodal  points.  The  tone 
produced  by  the  vibrations  of  the  whole  length  of 
a  string  is  called  its  fundamental  tone.  The  tones 
produced  by  the  vibrations  of  the  segments  of  a 
string  are  called  its  overtones  or  harmonics. 

(a.)  The  fact  that  a  string  may  thus  vibrate  in  segments,  with  the 
further  fact  that  a  string,  or  other  sounding  body,  can  hardly  be  made 
to  vibrate  as  a  whole  without  vibrating  in  segments  at  the  same  time, 
furnishes  a  means  of  explaining  quality  or  timbre  of  sound.  (§  492.) 

525.  Fundamental    Tones.  —  When    a    string 
vibrates  so  as  to  produce  its  fundamental  tone,  its  extreme 

positions  may  be  represented 
by  the  continuous  and  the 
FlG-  28a  dotted  lines   of    Fig.    280. 

This  effect  is  obtained  by  leaving  the  string  free  and 
bowing  it  near  one  of  its  ends.  If  a  number  of  little 
strips  of  paper,  doubled  in  the  middle,  be  placed  like  riders 
upon  the  string,  and  the  string  bowed  as  just  described, 
all  of  the  riders  will  be  thrown  up  and  most  of  them  off. 
This  shows  that  the  whole  string  vibrates  as  one  string ; 
that  there  is  no  part  of  it  between  the  fixed  ends  that  is 
not  in  vibration. 

526.  The  First  Overtone.— If  the  string  of  the 
sonometer  be  touched  exactly  at  its  middle  with  a  finger, 
or  better,  with  a  feather,  a  higher  tone  is  produced  when 
the  string  is  bowed.    This  higher  tone  is  the  octave  of  the 
fundamental.     The  string  now  vibrates  in  such  a  way  that 
the  point  touched  remains  Own 

at  rest.     Its  extreme  posi-  •~f~~~~         ~~~^»*~~~  ^ 

tions  may  be  represented  FlG-  2Sl- 

by  the  lines  of  Fig.  281.  The  point  N  is  acted  upon  by 
two  equal  and  opposite  forces ;  it  is  urged  to  move  both 


FUNDAMENTALS  AND  HARMONICS.  403 

ways  at  the  same  time  and,  consequently,  does  not  move 
at  all,  but  remains  at  rest  as  a  node.  The  tone  is  due  to 
the  vibrations  of  the  two  halves  of  the  string,  which  thus 
give  the  octave  instead  of  the  fundamental.  The  existence 
of  the  node  and  segments  will  continue  for  some  time  after 
the  finger  is  removed.  If  riders  be  placed  at  (7,  JVand  Z), 
the  one  at  N  will  remain  at  rest  while  those  at  G  and  D 
will  probably  be  dismounted. 

527.  Higher  Overtones.— In  like  manner,  if  the 
vibrating  string  be  touched  at  exactly  one-third,  one-fourth 


FIG.  282. 


or  one-fifth  of  its  length  from  one  end,  it  will  divide  into 
three,  four  or  five  segments,  with  vibrations  three,  four  or 
five  times  as  rapid  as  the  fundamental  vibrations.  If 
touched  at  one-third  its  length,  as  represented  in  Fig.  282, 
the  tone  will  be  the  fifth  to  the  octave  of  the  fundamental ; 


404 


QUALITY  OF  SOUND. 


if  touched  at  one-fourth  its  length,  the  tone  will  be  the 
second  octave  above.  Of  course,  any  other  aliquot  part  of 
the  length  of  the  string  may  be  used.  In  any  case,  the 
experiment  with  riders  may  be  repeated  to  indicate  the 
position  of  the  segments  and  nodes. 

528.  Qnality  or  Timbre. — As  a  sounding  body 
vibrates  as  a  whole  and  in  segments  at  the  same  time,  the 
fundamental  and  the  harmonics  blend.  The  resultant 
effect  of  this  blending  of  fundamentals  and  harmonics  con- 
stitutes what  we  call  the  quality  or  timbre  of  the  sound. 
We  recognize  the  voice  of  a  friend,  not  by  its  loudness  nor 
by  its  pitch,  but  by  its  quality.  When  a  piano  arid  violin 
sound  the  same  tone,  we  easily  distinguish  the  sound  of 
one  from  that  of  the  other,  because,  while  the  fundamentals 
are  alike,  the  harmonics  are  different.  Hence,  the  total 
effects  of  the  fundamentals  and  the  harmonics,  or  the 
qualities,  are  different.  The  possible  combinations  of  fun- 
damentals and  harmonics,  or  forms  of  vibratory  motion, 
are  innumerable. 

Experiment  16. — Take  your  seat  before  the  key-board  of  a  piano. 
Press  and  hold  down  the  key  of  "middle  C,"  marked  1  in  Fig.  283, 


which  represents  part  of  the  key -board.  This  will  lift  the  damper 
from  the  corresponding  piano  wire  and  leave  it  free  to  vibrate. 
Strongly  strike  the  key  of  C",  an  octave  below.  Hold  this  key  down 
for  a  few  seconds  and  then  remove  the  finger.  The  damper  will 
fall  upon  the  vibrating  wire  and  bring  it  to  rest.  When  the  sound 
of  0'  has  died  away,  a  swuid  of  higher  pitch  is  heard.  The  tone 


ANALYSIS  OP  SOVtf&S.  405 

Corresponds  to  the  wire  of  1,  which  wire  is  now  vibrating.  These 
vibrations  are  sympathetic  with  those  that  produced  the  first  over- 
tones of  the  wire  that  was  struck.  These  vibrations  in  the  wire  of 
1  prove  the  presence  of  the  first  overtone  in  the  vibrating  wire  of  C'. 
(See  §  509.) 

In  similar  manner,  successively  raise  the  dampers  from  the  wires 
of  2,  3,  4,  5,  6  and  7,  striking  C'  each  time.  These  wires  will  accu- 
mulate the  energy  of  the  waves  that  correspond  to  the  respective 
overtones  of  the  wire  of  C'  and  give  forth  each  its  'proper  tone. 
Thus  we  analyze  the  sound  of  the  wire  of  C'  and  prove  that  at  least 
seven  overtones  are  blended  with  its  fundamental. 

Some  of  these  tones  of  higher  pitch,  thus  produced  by  vibrations 
sympathetic  with  the  vibrations  of  the  segments  of  the  wire  of  C",  are 
feebler  than  others.  This  shows  that  the  quality  of  a  tone  depends 
upon  the  relative  intensities  as  well  as  the  number  of  the  overtones 
that  blend  with  the  fundamental. 

529.  Simple  and  Compound   Tones.  —  The 

well  trained  ear  can  detect  several  sounds  of  different 
pitch  when  a  single  key  of  a  piano  is  struck.  In  other 
words,  the  sound  of  a  vibrating  piano  wire  is  a  compound 
sound.  The  sound  of  a  tuning-fork  is  a  fairly  good 
example  of  a  simple  sound.  Simple  sounds  all  have  the 
same  quality,  differing  only  in  loudness  and  pitch. 

(a.)  A  series  of  Helrnholtz's  resonators  enables  the  student  of 
acoustics  to  analyze  any  compound  sound.  Each  component  tone 
may  be  reproduced  by  a  tuning-fork  of  appropriate  pitch.  By 
sounding  simultaneously  the  necessary  number  of  forks,  each  of 
proper  pitch  and  with  appropriate  relative  intensity,  Helmholtz 
showed  that  the  sounds  of  musical  instruments,  including  even  the 
most  wonderful  one  of  all  (the  human  voice),  may  be  produced 
synthetically. 

530.  Classes    of   Musical    Instruments. — 

Musical  instruments  may  be  divided  into  two  classes, 
stringed  instruments  and  wind  instruments.  The  sounds 
sent  forth  by  stringed  instruments  are  due  to  the  regular 
vibrations  of  solids ;  those  sent  forth  by  wind  instruments, 


406  MUSICAL 


to  the  regular  vibrations  of  columns  of  air  confined  in 
sonorous  tubes. 

531.  Sonorous  Tubes.—  The  material  of  which  a 
sonorous  tube  is  made  does  not  affect  the  pitch  or  loud- 
ness   of  the   sound,    but  does  determine  its   timbre    or 
quality.     Sonorous  tubes  are  called  mouth  pipes  or  reed 
pipes,  according  to  the  way  in  which  the  column  of  air  is 
made  to  vibrate. 

532.  Stopped  Pipes.  —  A.  sonorous  tube  may  have 
one  end  stopped  or  both  ends  open.     In  either  case,  the 
tones  are  due  to  waves  of  condensation  and  rarefaction 
transmitted  through  the  length  of  the  tube.     In  a  stopped 
pipe,  the  air  particles  at  the  closed  end  have  no  oppor- 
tunity for  vibration  ;  this  end  of  the  tube  is,  therefore,  a 
node.     The  mouth  of  the  tube  affords  opportunity  for  the 
greatest  amplitude.      The  length  of  such  a  pipe  is  one- 
fourth  the  wave  length  of  its  fundamental  tone. 

533.  Open    Pipes.  —  In   an    open  pipe,  the    ends 
afford  opportunity  for  the  greatest  amplitude  ;  the  node 
will  fall  at  the  middle.     The  air  column  will  now  equal 
one-half  the  wave   length;   the  tone  will   be   an   octave 
higher  than  that  produced  by  a  stopped  pipe  of  the  same 
length. 

534.  Organ  Pipes.  —  The  organ  pipe  affords   the 
best  illustration  of  mouth  pipes.     Fig.  284  represents  the 
most  common  kind  of  organ  pipe,  which  may  be  of  wood 
or  metal,  rectangular  or  cylindrical.    The  air  current  from 
the  bellows  enters  through  P,  passes  into  a  small  chamber, 


MUSICAL  INSTRUMENTS. 


407 


emerges  through  the  narrow  slit,  i,  and  escapes  in  puffs 

between  a  and  I,  the  two  lips  of  the  mouth.     The  puffs 

are  due  to  the  fact  that  the  air  cur-  M 

rent  from  i  strikes  upon  the  bevelled 

lip,  a,  and  breaks  into  a  flutter.     The 

puffing  sound  thus  produced  consists 

of  a  confused  mixture  of  many  faint 

sounds.     The  air  column  of  the  pipe 

can    resound   to   only  one   of   these 

tones.      The    resonance   of   the    air 

column,  brought  about  in  this  way, 

constitutes  the  tone  of  the  pipe. 


(a.)  We  see,  from  the  above,  that  it 
makes  little  difference  how  the  pulses  of 
air  are  produced.  A  vibrating  tuning-fork 
held  at  the  mouth  of  a  pipe  of  the  same 
pitch  is  enough  to  make  the  pipe  sound 
forth  its  tone.  The  production  of  the  tone 
is  strictly  analogous  to  the  phenomena 
mentioned  in  §  513. 


535.  Reed   Pipes. — A  simple 
reed  pipe  may  be  made  by  cutting 
a  piece  of  wheat  straw  eight  inches  (20  cm.)   long   so 
as  to  have  a  knot  at  one  end.      At  r,  about  an  inch 


FIG.  285. 

from  the  knot,  cut  inward  about  a  quarter  of  the  straw's 
diameter;  turn  the  knife-blade  flat  and  draw  it  toward 
the  knot.  The  strip,  rr',  thus  raised  is  a  reed  ;  the  straw 
itself  is  a  reed  pipe.  When  the  reed  is  placed  in  the 
mouth,  the  lips  firmly  closed  around  the  straw  between 


408  MUSICAL  INSTRUMENTS. 

r  and  s  and  the  breath  driven  through  the  apparatus,  the 
reed  vibrates  and  thus  produces  vibrations  in  the  air  col- 
umn of  the  wheaten  pipe.  Notice  the  pitch  of  the  musical 
sound  thus  produced.  Cut  off  two  inches  from  the  end 
of  the  pipe  at  s.  Blow  through  the  pipe  as  before  and 
notice  that  the  pitch  is  raised.  Cut  off,  now,  two  inches 
more,  and  upon  sounding* the  pipe  the  pitch  will  be  found 
to  be  still  higher.  We  thus  see  that  the  pipe  and  not  the 
reed  determines  the  pitch.  In  these  three  cases  we  had 
the  same  reed  which  was  obliged  to  adapt  itself  to  the 
different  vibrations  of  the  different  air  columns. 

(a.)  It  will  be  easily  seen  how  reeds  may  be  used  in  musical 
instruments.  The  accordeon,  clarionet  and  vocal  apparatus  are  reed 
instruments. 

536.    Effect   of  Lateral   Openings.  —  Certain 

wind  instruments,  like  the  flute,  fife  and  clarionet,  have 
holes  in  the  sides  of  the  tube.  On  opening  one  of  these 
holes,  opportunity  is  given  for  greatest  amplitude  at  that 
point.  This  changes  the  distribution  of  nodes,  affects  the 
length  of  the  segments  of  the  vibrating  air  columns,  and 
thus  determines  the  wave  length  or  pitch  of  the  tone. 

EXERCISES. 

1.  If  a  musical  sound  be  due  to  144  vibrations,  to  how  many  vibra- 
tions will  its  3d,  5th  and  octave,  respectively,  be  due? 

2.  Determine  the  length  of  a  tube  open  at  both  ends  that  can 
resound  to  the  tone  of  a  tuning-fork  vibrating  512  times  a  second. 

3.  A  certain  string  vibrates  100  times  a  second,     (a.)  Find  the 
number  Of  vibrations  of  a  similar  string,  twice  as  long,  stretched 
by  the  same  weight.     (6.)  Of  one  half  as  long. 

4.  A  certain  string  vibrates  100  times  per  second.     Find  the  num- 
ber of  vibrations  of  another  string  that  is  twice  as  long  and  weighs 
four  times  as  much  per  foot  and  is  stretched  by  the  same  weight. 

5.  A  musical  string  vibrates  200  times  a  second.     State  (a.)  what 


EXERCISES.  409 

takes  place  when  the  string  is  lengthened  or  shortened  with  no 
change  of  tension,  and  (&.)  what  change  takes  place  when  the  tension 
is  made  more  or  less,  the  length  remaining  the  same. 

6.  A  tube  open  at  both  ends  is  to  produce  a  tone  corresponding 
(a.}  to  32  vibrations  per  second.     Taking  the  velocity  of  sound  as 
1120  ft.,  find  the  length  of  the  tube.     (6.)  If  the  number  of  vibra- 
tions be  4480,  find  the  length  of  the  tube. 

7.  (a.)  Find  the  length  of  an  organ  pipe  whose  waves  are  four 
feet  long,  the  pipe  being  open  at  both  ends.     (&.)  Find  the  length, 
the  pipe  being  closed  at  one  end. 

8.  A  tuning-fork  produces  a  strong  resonance  when  held  over  a 
jar  15  inches  long,    (a.)  Find  the  wave  length  of  the  fork.    (&.)  Find 
the  wave  period. 

9.  If  two  tuning-forks  vibrating  respectively  256  and   259  times 
per  second  be  simultaneously  sounded  near  each  other,  what  phe- 
nomena would  follow  ? 

10.  A  musical  string,  known  to  vibrate  400  times  a  second,  gives 
a  certain  tone.     A  second  string  sounded  a  moment  later  seems  to 
give  the  same  tone.     When  sounded  together,  two  beats  per  second 
are  noticeable,     (a.)  Are  the  strings  in  unison?     (&.)  If  not,  what  is 
the  rate  of  vibration  of  the  second  string  ? 

11.  If  a  tone  be  produced  by  256  vibrations  per  second,  what  num- 
bers will  correspond  to  its  third,  fifth  and  octave  respectively  ? 

12.  If  a   tone  be  produced  by  264  vibrations  per  second,  what 
number  will  represent  the  vibrations  of  the  tone  a  fifth  above  its 
octave.  Ans.  792. 

Recapitulation. — In  this  section  we  have  considered 
the  Telephone  and  Phonograph ;  Sympa- 
thetic Vibrations  and  the  Resonance  of 
Sounding  Boards  and  Air  Columns  ;  Re- 
inforcement and  Interference  of  superposed 
waves,  including  the  phenomenon  of  Beats ;  Vi- 
brating Strings  ;  The  Musical  Scale  and  its 
relation  to  Number  of  Vibrations  and  Pitch  ; 
Timbre  and  its  dependence  upon  Fundamentals 
and  Harmonies  ;  Simple  and  Compound 
Tones,  their  Synthesis  and  Analysis;  Musi- 
cal Instruments 


410  REVIEW. 


REVIEW  QUESTIONS  AND  EXERCISES. 

1.  (a.)  Define  sound  ;  (b.)  give  its  cause;  (c.)  mode  of  propagation 
and  (d.)  velocity. 

2.  (a.)  Give  the  rate  at  which  sound  is  transmitted  in  air.     (6.) 
How  is  it  affected  by  temperature?    (c.)  Give  the  law  of  Reflection. 
(d.)  How  may  it  be  illustrated? 

3.  (a.)  What  is  capillary  attraction  ?    (b.)  Give  three  illustrations 
of  the  importance  of  capillary  action  in  the  operations  of  nature. 

4.  (#.)  Describe  an  experiment  showing  the  expansibility  of  the 
air.     (b.)  Give  the  laws  of  the  Pendulum. 

5.  (a.)  On  what  does  the  loudness  of  sound  depend?    (6.)  How 
may  the  pitch  of  strings  be  varied  ?     (c.)  Give  the  relative  number 
of  vibrations  in  the  major  diatonic  scale  and  (d.)  find  the  number  of 
vibrations  for  A2. 

6.  (a.)  Represent  by  a  diagram,  a  lever  of  the  first  class,  in  which 
one  pound  will  balance  five.     (&.)  Give  the  laws  of  falling  bodies. 

7.  Explain  the  Artesian  well  by  a  diagram. 

8.  (a.)  What  will  be  the  momentum  of  a  ball  weighing  two  ounces 
after  falling  4^  seconds  ?    (b.)  A  stone  weighing  20  Ib.  on  the  sur- 
face of  the  earth,  would  weigh  how  much  at  an  elevation  of  2000 
miles  from  the  surface  ? 

9.  Define  (a.}  wave  length ;   (6.)  wave  period ;  (c.)  amplitude  of 
vibration  ;  (d.)  phase  of  a  vibrating  particle. 

10.  (a.)  What  would  be  the  effect  of  making  a  small  hole  at  the 
highest  point  of  a  siphon  in  action  ?    (6.)  What  effect  upon  the  action 
of  a  siphon  would  be  produced  by  carrying  it  up  a  mountain?     (c.) 
What  effect  would  follow  if  the  atmosphere  were  suddenly  to  become 
denser  than  the  liquid  being  moved  ? 

11.  Describe  (a.)  a  complete  sound  wave  and  (6.)  its  manner  of 
propagation,     (c.)  How  does  the  transmission  of  sound  through  a 
smooth  tube  differ  from  its  transmission  through  the  open  air  ? 

12.  Give  the  laws  for  pressure  of  liquids  and  explain  each  by 
some  fact  or  experiment. 

13.  (a.)  Distinguish  clearly  between  noise  and  music.     (6.)  What 
is  meant  by  timbre  ?    (c.)  By  pitch  ? 

14.  Give   three  examples   of  musical  sounds  that   agree   in  one 
and  differ  in  two  elements  or  characteristics,  making  a  different  ele- 
ment agree  each  time. 

15.  Give  three  examples  of  musical  sounds  that  differ  in  one  and 
agree  in  two  elements,  making  a  different  element  differ  each  time. 


REVIEW.  411 

16.  (a.)  What  are  sympathetic  vibrations  ?     (&.)  How  may  they  be 
produced?    (c.)  What  are  beats ?    (d.)  How  may  they  be  produced  1 

17.  (a.)  What  is  Archimedes'  Principle  ?    (b.)  How  is  it  applied  in 
finding  the  specific  gravity  of  a  solid  ? 

18.  How  much  water  per  hour  will  be  delivered  from  an  orifice  of 
2  inches  area  49  feet  below  the  surface  of  a  tank  kept  full  ? 

19.  Describe  the  telephone. 

20.  (a.)  Describe  the  electrophorus.     (6.)  Explain  its  action. 

21.  (a.)  Describe  an  organ  pipe.     (&.)  Make  a  reed  pipe. 

22.  (a.)  Explain   the    charging    of    the   Leyden  jar;    (b.)  when 
charged,  what  is  the  electric  condition  of  the  outside  and  inside  of 
the  jar? 

23.  (a.)  A  body  falls  for  six  seconds ;  find  the  distance  traversed 
in  the  last  two  seconds  of  its  fall,     (b.)  How  far  will  a  body  fall  in 
Ta0  of  a  second  beginning  at  the  end  of  four  seconds?    (c.)  Explain 
the  "  kick  "  of  a  gun. 

24.  (a.)  Show  that  if,  in  an  Attwood's  machine,  one  weight  be  f 
as  heavy  as  the  other,  its  increment  of  velocity  will  be  £  that  of  a 
freely  falling  body,     (b.)  That  if  the  lighter  weight  be  f   of  the 
heavier,  its  increment  of  velocity  will  be  |  g. 

25.  A  telegraph  line  from  New  York  City  to  Meadville,  Pa.,  is  510 
miles  long.     The  wire  has  a  resistance  of  4  ohms  per  mile.     There 
are,  on  this  line,  19  relays  of  150  ohms  each  and  one  repeater  of  250 
ohms.     The  current  is  supplied  by  a  series  of  40  gravity  cells  with 
an  E.  M.  F.  of   1  volt  each.     Suppose  that  the   battery   and  the 
ground  and  other  connections  offer  a  resistance  of  574  ohms.     What 
is  the  strength  of  the  current  ?  Ans.  7  milliamperes. 

26.  Explain  the  electrical  phenomena  described  in  §  323  (b). 

27.  An  arc  lamp  has  a  difference  of  potential  of  36  volts  between 
the  carbon  tips.     The  resistance  of  the  arc  is  3.6  ohms,    (a.)  What 
is  the  current  strength  ?    (b.)  What  amount  of  heat  is  developed  in 
the  arc  per  second. 

Ans.  (a.)  10  amperes  ;  (b.)  86.4  lesser  calories. 

28.  A  coil  of  fine  wire  with  a  resistance  of  46.64  ohms  was  placed 
in  100  grams  of  ice-cold  water.      A  current  from  a   varies  of  50 
voltaic  cells  was  sent  through  the  wire  for  10  minutes.     Each  cell 
had  an  E.  M.  F.  of  1  volt  and  a  resistance  of  6  ohms.     [The  water 
would  not  short  circuit  the  wire.     See  Appendix  K  (2)].     (a.)  What 
was  the  current  strength  ?    (6.)  Find  the  rise  of  temperature  of  the 
water  assuming  that  no  heat  is  lost  by  the  water. 

Ans.  (a.)  0.144  amperes  ;  (6.)  1.39°  C. 


H  EAT. 


X8>M»ECTK)N  I. 

J\. 

TEMPERATURE,   THERMOMETERS,    EXPANSION. 

537,  Introductory  Quotation.—"  There  are  other  forces 
besides  gravity,  and  one  of  the  most  active  of  these  is  chemical  affin- 
ity.    Thus,  for  instance,  an  atom  of  oxygen  has  a  very  strong  attrac- 
tion for  one  of  carbon,  and  we  may  compare  these  two  atoms  to  the 
<  arth  and  a  stone  lodged  upon  the  top  of  a  house.     Within  certain 
limits,  this  attraction  is  intensly  powerful,  so  that  when  an  atom  of 
carbon  and  one  of  oxygen  have  been  separated  from  each  other,  we 
have  a  species  of  energy  of  position  just  as  truly  as  when  a  stone 
has  been  separated  from  the  earth.     Thus  by  having  a  large  quan- 
tity of  oxygen  and  a  large  quantity  of  carbon  in  separate  states,  we 
are  in  possession  of  a  large  store  of  energy  of  position.     When  we 
allowed  the  stone  and  the  earth  to  rush  together,  the  energy  of 
position  was  transformed  into  that  of  actual  motion  (§  159),  and  we 
should  therefore  expect  something  similar  to  happen  when  the 
separated  carbon  and  oxygen  are  allowed  to  rush  together.    This 
takes  place  when  we  burn  coal  in  our  fires,  and  the  primary  result, 
as  far  as  energy  is  concerned,  is  the  production  of  a  large  amount  of 
heat.     We  are,  therefore,  led  to  conjecture  that  heat  may  denote  a 
motion  of  particles  on  the  small  scale  just  as  the  rushing  together  of 
the  stone  and  the  earth  denotes  a  motion  on  the  large.     It  thus 
appears  that  we  may  have  invisible  molecular  energy  as  well  as 
visible  mechanical  energy." — Balfour  Stewart. 

538.  What    is    Heat  t—Heat  is  a  form  of  en- 
ergy.   It  consists  of  vibratory  motions  of  the  mole- 
cules of  matter  or  results  from  such  motions,  and 


TEMPERATURE.  413 

gives  rise  to  the  well  known  sensations  of  warmth 
and  cold.  By  means  of  these  effects  upon  the  animal 
body  it  is  generally  recognized.  Being  a  form  of  energy, 
it  is  a  measurable  quantity  but  not  a  material  substance. 

539.  What  is   Temperature  I—The  tempera- 
ture of  ct  body  is  its  state  considered  with  refer- 
ence to  its  ability  to  communicate  heat  to  other 
bodies.    It  is  a  term  used  to  indicate  how  hot  or  cold 
a  body  is.     When  a  body  receives  heat  its  temperature 
generally  rises,   but  sometimes  a   change    of   condition 
(§  53)  results  instead.    When  a  body  gives  up  heat,  its 
temperature  falls  or  its  physical  condition  changes. 

540.  An  Unsafe  Standard. — When  we  put  a  very  warm 
hand  into  water  at  the  ordinary  temperature,  we  say  that  the  water 
is  cold.     If  another  person  should  put  a  very  cold  hand  into  the 
Bame  water  he  would  say  that  the  water  is  warm.     If  a  person  place 
one  hand  in  water  freezing  cold  and  the  other  hand  in  water  as  hot 
as  he  can  endure,  and,  after  holding  them  there  some  time,  plunge 
them  simultaneously  into  water  at  the  ordinary  temperature,  the 
hand  from  tlje  cold  water  feels  warm  while  the  hand  from  the  hot 
water  feels  cold.     These  experiments  show  that  bodily  sensations 
cannot  be  trusted  to  measure  this  form  of  energy  that  we  call  heat. 

541.  Thermometers.  —  An  instrument  for 
measuring  temperature  is  called  a  thermometer. 
The  mercury  thermometer  is  the  most  common.  Its  ac- 
tion depends  upon  the  facts  that  heat  expands  mercury 
more  than  it  does  glass,  and  that  when  two  bodies  of  dif- 
ferent temperatures  are  brought  into  contact,  the  warmer 
one  will  give  heat  to  the  colder  one  until  they  have  a  com- 
mon temperature. 

542.  Graduation  of  Thermometers. — Ther- 
mometers are  graduated  in  different  ways,  but  in  all  cases 
there  are  two  fixed  points,  viz.,  the  freezing  and  the  boiling 


414 


TEMPERATURE. 


FIG.  286. 


points  of  water ;  or,  more  accurately,  the  temperature  of 
melting  ice  and  the  temper- 
ature of  steam  as  it  escapes 
from  water  boiling  under 
a  pressure  of  one  atmos- 
phere. 

543.       Determination 
of  the  Freezing  Point.— 

Ice  in  contact  with  water  cannot 
be  raised  above  a  certain  tem- 
perature ;  water  in  contact  with 
ice  cannot  be  reduced  below  the 
same  temperature.  Here,  then, 
is  a  temperature  fixed  and  easily 
produced.  The  thermometer  is 
placed  in  melting  ice  or  snow 
contained  in  a  perforated  vessel. 
When  the  mercury  column  has  come  to  rest,  a  mark  is  made  on  the 
glass  tube  at  the  level  of  the  mercury.  This  point  is,  for  the  sake 
tf  brevity,  called  the  freezing  point. 

544.    Determination    of  the    Boiling    Point.— The 

temperature  of  steam  issuing  from  water  boiling  under  any  given 
pressure  is  invariable.  Fig.  287  represents  a  metal  vessel  in  which 
water  is  made  to  boil  briskly.  The  thermom- 
eter being  supported  as  represented  is  sur- 
rounded by  the  steam  but  does  not  touch  the 
water.  That  the  steam  may  not  cool  before 
it  comes  into  contact  with  the  thermometer, 
the  sides  of  the  vessel  are  surrounded  by  what 
is  called  a  "steam-jacket."  A  bent  tube  open 
at  both  ends  and  containing  mercury  in  the 
bend  is  sometimes  added.  When  the  mercury 
stands  at  the  same  level  in  both  arms,  the 
pressure  upon  the  surface  of  the  boiling  liquid 
is  just  equal  to  the  external  atmospheric  pres- 
sure, which  should  be  760  mm.  When  the 
mercury  column  has  come  to  rest,  a  mark  is 
made  on  the  glass  tube  at  the  level  of  the 
mercury.  This  point  is,  for  the  sake  of 
FIG.  287.  brevity,  called  the  boiling  point, 


TEMPERATURE.  415 

545.  Thermometric    Scales.  —  There   are    two 
ecales  used  in  this  country,  the  centigrade  and 
Fahrenheit's.  For  these  scales,  the  fixed  points,  de- 
termined as  just  explained,  are  marked  as  follows  t 

Centigrade*  Fahrenheit. 

Freezing  point,          0°  32° 

Boiling  point,         100°  212° 

The  tube  between  these  two  points  is  divided 
into  100  equal  parts  for  the  centigrade  scale  and 
into  180  for  Fahrenheit's.  Hence  a  change  of 
temperature  of  5°  0.  is  equal  to  a  change  of  9°  F., 
or  an  interval  of  one  centigrade  degree  is  equal  to 
FIG.  288.  an  interval  °f  -f  of  a  Fahrenheit  degree. 

546.  Thermometric    Readings.  —  To  change 
the  readings  of  a  centigrade  thermometer  to  those  of 
Fahrenheit's,  or  vice  versa,  is  a  little  more  complicated 
than  to  determine  the  relation  between  the  intervals  of 
temperature.     This  complication  arises  from  the  fact  that 
Fahrenheit's  zero  is  not  at  the  freezing  point  but  32  de- 
grees below.    To  reduce  Fahrenheit  readings  to  centigrade 
readings,  subtract  32  from  the  number  of  Fahrenheit  de- 
grees and  multiply  the  remainder  by  j. 


To  reduce  centigrade  readings  to  Fahrenheit  readings, 
multiply  the  number  of  centigrade  degrees  by  •$  and  add  33. 

F.  =  lc.  +  32. 
5 

(a.)  Suppose  that  we  desire  to  find  the  equivalent  centigrade 
reading  for  50°  P.  Subtracting  32,  we  see  that  this  temperature  is 
18  Fahrenheit  degrees  above  the  freezing  point.  But  one  Fahren- 
heit degree  being  equal  to  jj  of  a  centigrade  degree,  this  temperature 


416 


TEMPERA  TUR  E. 


is  f  of  18,  or  10  centigrade  degrees  above  the  freezing  point.  Henca 
the  reading  will  be  10°  C. 

(6.)  Suppose  that  we  desire  to  find  the  equivalent  Fahrenheit 
reading  for  45°  C.  This,  temperature  is  45  centigrade  degrees  above 
the  freezing  point,  or  81  Fahrenheit  degrees  above  the  freezing 
point.  Hence  the  reading  will  be  (81  +  32  =)  113°  F.  (See Fig.  288.) 

(e.)  The  centigrade  thermometer  is  the  most  convenient  and  is 
adopted  in  all  countries  as  the  standard  scale  for  scientific  reference 
Like  the  metric  system,  its  general  use  in  this  country  is  probab]} 
only  a  question  of  time. 

Note. — It  is  desirable  that  this  class  be  provided  with  several 
"chemical"  thermometers;  i.  e.,  thermometers  having  the  scale 
marked  on  the  glass  tube  instead  of  a  metal  frame. 

547.  Differential  Thermometer.— Leslie's  dif- 
ferential thermometer  (Fig.  289)  shows  the  difference  in 
temperature  of  two  neighboring  places  by 

the  expansion  of  air  in  one  of  two  bulbs. 
These  bulbs  are  connected  by  a  bent  glass 
tube  containing  some  liquid  not  easily 
volatile.  It  is  an  instrument  of  simple 
Donstruction  (See  Appendix,  M.)  and  great 
delicacy  of  action,  but  has  been  largely 
superseded  by  the  thermopile  and  galvan- 
ometer (§§414,391). 

548.  Expansion. — Heat   consists 
generally  of  molecular  vibrations.     "What-        FIG.  289. 
ever   raises    the  temperature  of  a  body 

increases  the  energy  with  which  the  molecules  of  that 
body  swing  to  and  fro.  These  molecules  are  too  small  (§  5), 
and  their  range  of  motion  too  minute  to  be  visible,  and  we 
must  call  upon  our  imaginations  to  make  good  the  defect 
of  our  senses.  We  must  conceive  these  invisible  molecules 
as  held  together  by  the  force  of  cohesion,  yet  vibrating 
to  and  fro.  The  more  intense  the  heat,  the  greater  the 


TEMPERA  TURE. 


417 


energy  of  these  molecular  motions.  Molecules  thus  vi- 
brating must  push  each  other  further  apart,  and  thus  cause 
the  body  which  they  constitute  to  expand.  This  expansion, 
or  increase  of  volume,  is  the  first  effect  of  heat  upon 
bodies. 

(a.)  Imagine,  if  possible,  twenty -five  quiet  boys  standing  closely 
crowded  together.  Upon  the  floor  draw  a  chalk  line  enclosing  the 
group.  If  these  boys  be  suddenly  set  shaking,  as  by  the  ague,  they 
will  force  some  of  their  number  over  the  chalk  line.  From  the 
motions  of  the  individuals  has  resulted  an  expansion  of  the  living 


549.  Expansion  Illustrated. — The  expansion  of 
solids  may  be  shown  by  a  ball,  which,  at  ordinary  tempera- 
tures, will  easily  pass  through  a 
ring ;  on  heating  the  ball  it  will 
no  longer  pass  through  the  ring. 
If  the  ball  be  cooled  by  plung- 
ing it  into  cold  water,  it  will 
again    pass  through    the   ring 
This  illustrates  the  increase  oi 
volume  or    cubical    expansion. 
Sometimes    the    expansion    in 
length  only  is  measured.     This 
is  called  linear  expansion.    Ex- 
pansion is  also  illustrated  in  the 

FIG.  290.  compensation  pendulum  (§  149). 

550.  Unequal  Expansion. — Different  substances 
expand  at  different  rates  for  the  same  change  of  temper- 
ature.     This  may  be  shown  by  heating  a  bar  made  by 
riveting  together,  side  by  side,  two  thin  bars  of  equal  size, 
one  of  iron  and  one  of  brass,  so  that  the  compound  bar 
shall  be  straight  at  the  ordinary  temperature.    As  brass 


ilS  TEMPERATURE. 

expands  and  contracts  more  than  iron,  when  the  compound 
bar  is  heated  it  will  curve  with  the  brass  on  the  convex 
eide ;  when  it  is  cooled,  it  will  curve  with  the  brass  on  the 
concave  side. 

(a.)  Glass  and  platinum  expand  nearly  alike.  In  fact,  the  rates 
of  expansion  are  so  nearly  alike  that  platinum  wires  may  be  fused 
into  glass  tubes,  as  is  done  in  electrolysis  apparatus  and  eudiometers. 
If  we  attempt  thus  to  fuse  copper  wire  into  glass,  the  glass  will  be 
bi«*ken  during  the  unequal  contraction  from  cooling. 

551.    Practical    Applications    of    Expansion.— The 

energy  of  expansion  and  contraction  of  solids,  when  heating  and 
cooling,  is  remarkable.  This  expansion  of  metals  by  heat  is 
ulilized  by  coopers  in  setting  hoops,  by  wheelwrights  in  setting 
tires,  and  by  builders  in  straightening  bulging  walls.  When  the 
iron  rails  of  our  railways  are  laid,  a  small  space  is  left  between  the 
endb  of  each  two  adjoining  rails  to  provide  for  their  inevitable 
expansion  by  the  summer  heat.  The  iron  tubular  bridge  over  the 
Menai  Straits  is  about  1800  feet  long.  Its  linear  expansion  is  abort 
one  foot,  and  is  provided  for  by  placing  the  ends  of  the  huge  tube 
upon  /oilers. 

552.  Expansion  of  Liquids. — The  expansion  of 
liquids  may  be  illustrated  as  follows :  Nearly  fill  a  Florence 
flask  with  water,  and  place  it  on  a  retort  stand  or  other 
convenient  support.     A  long  straw  is  supported  by  a  thread 
tied  near  one  end.    From  the  short  end  of  this  straw  lever 
is  suspended  a  weight  nearly  balanced  by  the  long  arm  of 
the  lever.     This  weight  hangs  in  the  neck  of  the  flask, 
and  rests  lightly  upon  the  surface  of  the  water  (§  238). 
By  placing  a  spirit-lamp  below  the  flask  the  water  may  be 
heated.     As  it  expands,  it  rises  in  the  neck  of  the  flask, 
raises  the  weight,  and  lowers  the  end  of  the  long  arm  of 
the  lever,  which  may  be  seen  to  move. 

553.  Anomalous   Expansion   of   Water.— 

Water  presents  a  remarkable  exception  to  the  general  rule. 
//  water  at  0°C.  b&  heated,  it  will  contract  until  it 


TEMPERATURE. 


419 


reaches  4°  C.,  its  temperature  of  greatest  density, 
Heated  above  this  point  it  expands. 

(a.)  Through  the  cork  of  a  large  flask  pass  a  fine  glass  tube.    Fill 
the  flask  with  water  at  the  ordinary  temperature,  and  insert  the 

cork  and  tube  so  that  the  water 
shall  rise  some  distance  in  the 
tube.  Place  the  flask  in  a  freezing 
mixture,  such  as  salt  and  pounded 
ice.  The  water  column  in  the 
tube  falls,  showing  that  the  water 
is  contracting.  But  before  the 
water  freezes  the  contraction 
ceases,  the  column  in  the  tube 
becomes  stationary,  and  then  be- 
gins to  rise  again.  This  shows 
that  water  does  not  contract  on 
being  cooled  below  a  certain  tem- 
perature, and  that  there  is  a  tern- 
perature  of  maximum  density 
above  the  freezing  point. 

(&.)  Fig.  291  represents  a  glass 
cylinder   with  two  thermometers 
inserted  in  the  side,  near  the  top 
and  bottom,  at  A  and  B.    Midway 
between  A  and  B  is  an  envelope  C,  which  may  be  filled  with  a 
sing  mixture.     The  envelope  being  empty,  the  cylinder  is  filled 


FIG.  291. 


420 


TEMPERA  TUEE. 


the  ice  would  sink  and  destroy  everything  living  in  the 
water.  The  entire  body  of  water  would  soon  become  a 
solid  mass  which  the  heat  of  summer  could  not  wholly 
melt,  for,  as  we  shall  soon  see,  water  has  little  power  to 
carry  heat  downward.  As  it  is,  in  even  the  coldest  winters, 
the  mass  of  water  in  our  northern  lakes  remains  at  a  tem- 
perature of  4°C.,  the  colder  water  floats  upon  the  warmer 
layer,  ice  forms  over  all,  and  protects  the  living  things 
below. 

555.  Expansion  of  Oases. — The  expansion  of 
gases  may  be  shown  by  partly  filling  a  bladder  with  cold 
air,  tying  up  the  opening,  and  placing  the  bladder  near 
the  fire.  The  expanded  air  will  fill  the  bladder.  Through 
the  cork  of  a  bottle  pass  a  small  glass  tube  about  a  foot 
iong.  Warm  the  bottle  a  little  between  the  hands  and 
place  a  drop  of  ink  at  the  end  of  the  tube.  As  the  air 
contracts  the  ink  will  move  down  the  tube  and  form  a 
frictionless  liquid  index. 
By  heating  or  cooling  the 
bottle  the  index  may  be 
made  to  move  up  or  down. 
If  a  closed  flask  having  a 
delivery  tube  terminating 
under  water  be  heated, 
some  of  the  expanded  air 
mil  he  forced  to  escape, 
and  may  be  seen  bubbling 
through  the  water.  By 
"collecting  over  water" 
the  air  thus  driven  out, 
it  may  be  accurately 
measured.  (Fig.  292.) 
14 


FIG.  292. 


TEMPERATURE.  421 

556.  Practical  Results.—  The  ascension  of  '  '  fire-balloons  " 
and  the  draft  of  chimneys  are  due  to  the  expansion  of  gases  by  heat 
When  the  air  in  the  chimney  of  a  stove  or  lamp  is  heated,  it  is  ren 
dered  lighter  than  the  same  bulk  of  surrounding  air,  and,  therefore, 
rises.  The  cooler  air  comes  in  to  take  its  place  and  thus  feeds  the  com- 
bustion.  Sometimes  when  a  fire  is  first  lighted,  the  chimney  is  so 
cold  that  the  current  is  not  quickly  established  and  the  smoke 
escapes  into  the  room.  But  in  a  little  while  the  air  column  rises 
and  the  usual  action  takes  place.  By  the  aid  of  a  good  thermometer 
it  may  be  shown  that  the  air  near  the  ceiling  of  a  room  is  warmer 
than  the  air  near  the  floor.  When  the  door  of  a  warmed  room  is 
left  slightly  ajar,  there  will  be  an  inward  current  near  the  floor  and 
an  outward  current  near  the  top  of  the  door.  These  currents  ma? 
be  shown  by  holding  a  lighted  candle  at  these  places.  Artificial 
ventilation  depends  upon  the  same  principles. 

557.  Rate  of  Gaseous  Expansion.—  The  rate 
of  expansion  is  practically  the  same  for  all  gases,  viz., 
0.00366  or  ^^  of  the  volume  at  0°  C.,  for  each  centigrade 
degree  that  the  temperature  is  raised  above  the  freezing 
point.  In  other  words,  a  liter  of  air  at  0°  C.,  expands  to 


1  I  +  .00366  I  at  1°  C., 
1  I  +  (.00366  x  2)  I  at  2°  0. 


(.00366  x3)?.at3°C., 
I  at  4°  C. 


Of  course,  if  we  use  Fahrenheit  degrees  the  expansion 
will  he  only  f  as  great,  or  about  :rJT.  A  litre  of  gas  at  32°  F. 
expands  to  1^  I  at  33°  F.  ;  to  ff  J  I  at  39°  F.,  etc. 


558.   Absolute  Zero  of  Temperature.—  The 

temperature  at  which  the  molecular  motions  con- 
stituting heat  wholly  cease  is  called  the  absolute 
zero.  It  has  never  been  reached,  and  has  been  only  ap- 
proximately determined,  but  it  is  convenient  as  an  ideal 
starting-point.  The  zero  point  of  the  thermometers  does 
not  indicate  the  total  absence  of  heat.  A  Fahrenheit 
thermometer,  therefore,  does  not  indicate  that  boiling 
water  is  212  times  as  hot  as  ice  at  1°  F.  ;  a  centigrade. 


422  TEMPERATURE. 

thermometer  does  not  indicate  that  boiling  water  has  100 
times  as  much  heat  as  water  at  1°  C. 

(a.)  Temperature,  when  reckoned  from  the  absolute  zero,  is  called 
absolute  temperature.  Absolute  temperatures  are  obtained  by  add- 
ing 460  to  the  reading  of  a  Fahrenheit  thermometer,  or  273  to  the 
reading  of  a  centigrade  thermometer. 

559.  Temperature,  Volume  and  Pressure.— 

By  raising  a  gas  from  0°0.  to  273°  C.,  its  volume  will  be 
doubled.  To  reduce  the  gas  at  this  temperature  to  its 
original  volume,  the  original  pressure  must  be  doubled. 
From  our  knowledge  of  pneumatics  and  gaseous  expansion, 
we  are  able  to  solve  certain  problems  relating  to  the  volume 
of  gases  under  different  pressures  and  temperatures. 

Examples.  —  (1.)  A  mass  of  air  at  0°  C.  and  under  an  atmos- 
pheric pressure  of  30  inches,  measures  100  cu.  inches  ;  what  will  be 
its  volume  at  40°  C.  under  a  pressure  of  28  inches  ?  First,  suppose 
the  pressure  to  change  from  30  inches  to  28  inches.  The  air  will 
expand,  the  two  volumes  being  in  the  ratio  of  28  to  30  (§  284).  In 
other  words,  the  volume  will  be  f-f  times  100  cubic  inches  or  107J 
cu.  in.  Next,  suppose  the  temperature  to  change  from  0°  C.  to 
40°  C.  The  expansion  will  be  ^  of  the  volume  at  0°  C.  ;  the  volume 
will  be  1^  of  the  volume  at  0°  C.  l-ffc  times  107£  cubic  inches 
=122£ff  inches.—  Ans. 

The  problem  may  be  worked  by  proportion  as  follows  : 
28  :  30     )  28:    30 


(2.)  At  150°  C.,  what  will  be  the  volume  of  a  gas  that  measures 
10  cu.  cm.  at  15°  C.  ? 

273  +  15  :  273  +  150  :  :  10  :  x.          .'.  x  =  14.69  cu.  cm. 
(3.)  If  100  cu.  cm.  of  hydrogen  be  measured  at  100°  C.  ,  what  will 
be  the  volume  of  the  gas  at  —100°  C.? 

273  +  100  :  273  -  100  :  :  100  :  x.      /.  x  =  46.37  cu.  cm. 


TEMPERATURE.  423 

(4.)  A  liter  of  air  is  measured  at  0°  C.  and  760  mm.   What  volume 
ill  it  occupy  at  740  mm.,  and  15.5°  C.  ? 

::  1,000:,.        .-.  .- M8S.M*. «. 
EXERCISES. 

1.  A  rubber  balloon,  capacity  of  1  liter,  contains  900  cu.  cm.  of 
oxygen  at  0°  C.     When  heated  to  30°  C.,  what  will  be  the  volume 
of  the  oxygen  ?  Ans.  998.9  cu.  cm. 

2.  If  170  volumes  of  carbonic  acid  gas  be  measured  at  10°  C.,  what 
will  be  the  volume  when  the  temperature  sinks  to  0°  C.  ? 

3.  A  certain  weight  of  air  measures  a  liter  at  0°  C.    How  much 
will  the  air  expand  on  being  heated  to  100°  C.?       Ans.  366.3  cu.  cm. 

4.  A  gas  has  its  temperature  raised  from  15°  C.  to  50°  C.     At  the 
latter  temperature  it  measures  15  liters.     What   was  its  original 
volume?  Ans.  13,374.6  cu.  cm. 

5.  A  gas  measures  98  cu.  cm.  at  185°  F.     What  will  it  measure  at 
10°  C.  under  the  same  pressure  ?  Ans.  77.47  cu.  cm. 

6.  To  what  volume  will  a  liter  of  gas  contract  in  cooling  from 
42°  F.  to  32°  F.?  Ans.  980  cu.  cm. 

7.  A  certain  quantity  of  gas  measures  155  cu.  cm.  at  10°  C.,  and 
under  a  barometric  pressure  of  530  mm.     What  will  be  the  volume 
at  18.7°  C.,  and  under  a  barometric  pressure  of  590  mm.l 

8.  A  gallon  of  air  (231  cu.  in.)  is  heated,  under  constant  pressure, 
from  0°  C.  to  60°  C.     What  was  the  volume  of  the  air  at  the  latter 
temperature  ?  Ans.  281.77  cu.  in. 

9.  A  fire  balloon  contains  20  cu.  ft.  of  air.     The  temperature  of 
the  atmosphere  being  15°  C.  and  that  of  the  heated  air  in  the  bal- 
loon being  75°  C.,  what  weight,  including  the  balloon,  may  be  thus 
supported?    (See  Appendix  G.)  Ans.  1,847  grains. 

10.  The  difference  between  the  temperatures  of  two  bodies  is 
36"  F.    Express  the  difference  in  centigrade  degrees. 

11.  The  difference  between  the  temperatures  of  two  bodies  is 
35°  C.    Express  the  difference  in  Fahrenheit  degrees. 

12.  (a.)  Express  the  temperature  68°  F.  in  the  centigrade  scale. 
(&.)  Express  the  temperature  20D  C.  in  the  Fahrenheit  scale. 

13.  What  will  be  the  tension  at  30°  C.  of  a  quantity  of  gas  which 
at  0°  C.  has  a  tension  of  a  million  dynes  per  sq.  cm.,  the  volume 
remaining  the  same  ?    (§  69.)  Ans.  1109890  dynes. 

14.  A  liter  of  gas  under  a  pressure  of  1013600  dynes  per  sq.  cm. 
is  allowed  to  expand  until  the  pressure  is  reduced  to  1000000  dynes 
per  sq.  cm.     At  the  same  time,  the  temperature  is  raised  from  0°  C 
to  100°  C.    Find  the  final  volume.     Ans.  1385  cu.  cm.  nearly. 


424  LIQUEFACTION. 

Recapitulation. — In  this  section  we  have  considered 
the  Nature  of  Heat;  the  meaning  of  Tem- 
perature ;  Thermometers  and  their  graduation  -, 
the  determination  of  the  Freezing  and  Boiling 
Points ;  thermometric  Scales  and  Readings ; 
the  Differential  Thermometer  ;  Expansion 
of  Solids  ;  Expansion  of  Liquids,  especially 
the  Expansion  of  Water  ;  the  Expansion  of 
Gases  and  the  Rate  thereof;  Absolute  Zero  of 
temperature;  the  relation  between  Temperature, 
Pressure  and  Volume. 


ECTION  II. 


LIQUEFACTION,    VAPORIZATION,    DISTILLATION. 

56O.  Liquefaction. — In  the  last  section  we  learned 
that  heat  is  a  form  of  energy.  As  energy,  it  is  able  to 
perform  work,  such  as  overcoming  or  weakening  the  force 
of  cohesion.  It  is  well  known  that  when  a  solid  is  changed 
to  the  liquid  or  aeriform  condition,  or  when  a  liquid  is 
changed  to  a  vapor,  it  is  done  by  an  increase  of  heat,  and 
that  when  the  reverse  operations  are  performed,  it  is  by  a 
diminution  of  heat.  Cohesion  draws  the  particles  together ; 
heat  pushes  them  asunder,  and  on  the  varying  preponder- 
ance of  one  or  the  other  of  these  antagonistic  powers,  the 
condition  of  the  body  seems  to  depend.  When  the  firm 
grip  of  cohesion  has  been  so  far  weakened  by  heat  that  the 
molecules  easily  change  their  relative  positions  (§  55),  the 
body  passes  from  the  solid  into  the  liquid  condition.  This 
change  of  condition  is  called  liquefaction. 


LIQ  UEFA  CTIO& 


425 


561.  Laws  of  Fusion. — It  has  been  found  by 
experiment  that  the  following  statements  are  true : 

(1.)  Every  solid  begins  to  melt  at  a  certain  temperature 
vrfrich  is  invariable  for  the  given  substance  if  the  pressure 
be  constant.  When  cooling,  the  substance  will  solidify  at 
the  temperature  of  fusion. 

(2.)  The  temperature  of  the  solid,  or  liquid,  remains  at 
the  melting  point  from  the  moment  that  fusion  or  solidi- 
fication begins  until  it  is  complete. 

(a.)  If  a  flask  containing  ice  be  placed  over  a  fire,  it  will  be  found 
that  the  hotter  the  fire  the  more  rapid  the  liquefaction,  but  that  if 
the  contents  of  the  flask  be  continually  stirred,  the  thermometei 
will  remain  at  0°  C.  until  the  last  bit  of  ice  is  melted  (§  543-).  If 
sulphur  be  used  instead  of  ice,  the  tem- 
perature will  remain  at  115°  C.  until  the 
sulphur  is  all  melted.  (Fig.  293.) 

5O2.  Reference  Table  of  Melt* 
ing-  Points : 

Alcohol,     ....       Never  frozen. 
Mercury,      ....        — 38.8°C. 
Sulphuric  acid,   -     -  — 344 

Ice, ^'^          0. 

Sulphur,    ....  115. 

Lead,        326 

Zinc,      ....  425 

Silver  (pure),     -    -    -        1,000 
Gold  (pure),     -  1,250 

Iron  (wrought),      -     -       1,600 

P  Note. — The  higher  temperatures  in  this 

table    are    only    approximate.       Certain 

bodies  soften  and  become  plastic  before  they  melt.     In  this  condition 

glass  is  worked  and  iror.  is  welded. 

563.  Vaporization. — If,  after  liquefaction,  further 
additions  of  heat  be  made,  a  point  will  be  reached  at  which 
the  heat  will  overbalance  both  the  cohesion  and  the 
pressure  of  the  atmosphere  and  the  liquid  pass  into  the 
aeriform  condition.  This  change  of  form  is  called  vapor 


426 


VAPORIZA  TION. 


ization.    Vaporization  may  be  of  two  kinds — evaporation 
and  ebullition. 

564.  Evaporation. — Evaporation    signifies  the 
quiet   formation    of  vapor    at    the    surface    of   a 
liquid. 

(a.)  With  reference  to  the  rapidity  with  which  evaporation  takes 
place,  it  may  be  remarked  that— 

(t.)  It  varies  with  the  temperature. 
(2.)  It  varies  with  the  extent  of  surface. 

(3.)  It  varies  with  pressure  upon  the  liquid,  being  exceedingly 
rapid  in  a  vacuum. 

565.  Evaporation  in  Vacuo. — The  rapid  forma- 
tion of  vapors  in  a  vacuum  is  prettily  illustrated  by  the 
following     experiment : 

Torricellian  vacua  are 
formed  at  the  top  of  four 
barometer  tubes,  A,  B, 
tfandD,  Fig.  294.  Into 
the  mouth  of  B  pass  a 
few  drops  of  water.  They 
will  rise  through  the  mer- 
cury to  the  vacuum  at 
the  top.  Upon  reaching 
this  open  space  they  are 
instantly  vaporized.  The 
tension  of  the  aqueous 
vapor  shows  itself  by 
lowering  the  mercury 
column.  This  depression 
is  due  to  the  tension 

rather  than  to  the  weight 

FIG.  294. 
of  the  vapor,  because  the 

water  weighs  scarcely  anything  compared  with  the  mer 


VAPORIZA  TION. 


427 


cury  it  displaces.  Introducing  the  same  quantity  of 
alcohol  into  C,  and  of  ether  into  D,  they  are  instantly 
vaporized,  but  the  mercury  will  be  depressed  more  by  the 
alcohol  than  by  the  water,  and  more  by  the  ether  than  by 
the  alcohol. 

(a.)  At  the  beginning  of  the  experiment,  the  four  mercury 
columns  indicated  the  atmospheric  pressure ;  at  the  end  of  the 
experiment,  the  column  in  A  indicated  the  full  pressure  of  the 
atmosphere  ;  the  columns  in  B,  G  and  D  indicate  that  pressure 
minus  the  tension  of  their  respective  vapors.  This  experiment 
also  shows  that,  at  the  same  temperature,  the  vapors  of  different 
liquids  have  different  tensions. 

566.  Ebullition.— Ebullition,  or  boiling,  signi- 
fies the  rapid  formation  of  vapor  bubbles  in  the 

mass  of  a  liquid. 
When  a  flask  con- 
taining water  i? 
placed  over  the  flame 
of  a  lamp,  the  ab- 
sorbed air  that  is 
generally  to  be  found 
in  water  is  driven  off 
in  minute  bubbles 
that  rise  and  escape 
without  noise.  As 
the  temperature  of 
the  water  is  raised, 
the  liquid  molecules 
in  contact  with  the 
bottom  of  the  flask 

become  so  hot  that 
FIG.  295. 

the  heat  is  able  to 

overcome  the  cohesion  between  the  molecules,  the  pressure 


428  VA  PORIZA  TION. 

of  the  overlying  water,  and  the  pressure  of  the  atmosphere 
above  the  water.     Then  the  water  boils. 

(a.)  When  the  first  bubbles  of  steam  are  formed  at  the  bottom  of 
the  water,  they  rise  through  the  water,  condense  in  the  cooler  layers 
above,  and  disappear  before  reaching  the  surface.  The  formation 
and  condensation  of  these  bubbles  produce  the  peculiar  sound  known 
as  singing  or  simmering,  the  well-known  herald  of  ebullition. 
Finally,  the  water  becomes  heated  throughout,  the  bubbles  increase 
in  number,  grow  larger  as  they  ascend,  burst  at  the  surface,  and 
disappear  in  the  atmosphere.  The  whole  liquid  mass  is  agitated 
with  considerable  vehemence,  there  is  a  characteristic  noisy  accom- 
paniment, the  quantity  of  water  in  the  flask  diminishes  with  every 
bubble,  and  finally  it  all  disappears  as  steam.  The  water  has 
"  boiled  away." 

567.  Laws  of  Ebullition. — It  has  been  found  by 
experiment  that  the  following  statements  are  true : 

(1.)  Every  liquid  begins  to  boil  at  a  certain  temperature, 
which  is  invariable  for  the  given  substance  if  the  pressure 
be  constant.  When  cooling,  the  substance  will  liquefy  at 
the  temperature  of  ebullition,  or  at  the  boiling  point. 

(2.)  The  temperature  of  the  liquid,  or  vapor,  remains 
at  the  boiling  point  from  the  moment  that  it  begins  to 
boil  or  liquefy. 

(3.)  An  increase  of  pressure  raises  the  boiling  point ;  a 
decrease  of  pressure  lowers  the  boiling  point. 

(a.)  In  a  beaker  half  full  of  water,  place  a  ther- 
mometer and  a  test  tube  half  filled  with  ether. 
Heat  the  water.  When  the  thermometer  shows  a 
temperature  of  about  60°  C.,  the  ether  will  begin  to 
boil.  The  water  will  not  boil  until  the  temperature 
rises  to  100°  C.  The  temperature  will  not  rise  be- 
yond this  point. 
FIG.  296. 

568.  Vapor  Pressure.— The  pressure 
of  a  vapor  (§  282)  is  due  to  the  kinetic  energy  of  its  con- 
stituent molecules.  "  As  a  liquid  evaporates  is  a  closed 


VAPORIZATION.  429 

space,  the  vapor  formed  exerts  a  pressure  upon  the  enclosure 
and  upon  the  surface  of  the  liquid,  which  increases  as  long 
as  the  quantity  of  vapor  increases  and  reaches  a  maximum 
when  the  space  is  saturated.  This  maximum  pressure  of 
a  vapor  increases  with  the  temperature.  When  evapora- 
tion takes  place  in  a  space  filled  hy  another  gas  that  has 
no  action  upon  the  vapor,  the  pressure  of  the  vapor  is 
added  to  that  of  the  gas  and  the  pressure  of  the  mixture 
is,  therefore,  the  sum  of  the  pressures  of  its  constituents." 

569.  Effect  of  Pressure  upon  Boiling  Point. 

— We  saw  in  §  566  that  when  a  liquid  is  boiled,  the  heat 
has  three  tasks  or  three  kinds  of  work  to  perform,  viz., 
overcoming  cohesion,  liquid  and  atmospheric  pressures. 
Nothing  can  be  more  evident  than  the  propositions  that 
increasing  the  work  to  be  done  involves  an  increase  in  the 
energy  needed  to  do  the  work ;  that  decreasing  the  work 
to  be  done  involves  a  decrease  in  the  energy  needed  to  do 
the  work.  In  the  case  of  boiling  any  given  liquid,  the  first 
of  the  three  tasks  can  not  be  varied  ;  either  of  the  other 
two  easily  may.  If  we  increase  the  pressure,  we  increase 
the  work  to  be  done  and,  therefore,  increase  the  necessary 
amount  of  heat,  the  only  form  of  energy  competent  to  do 
the  work.  If  we  lower  the  pressure,  we  lessen  the  work  to 
be  done  and,  therefore,  lessen  the  necessary  amount  of 
heat.  This  means,  in  the  first  case,  raising  the  boiling 
point ;  in  the  second  case,  lowering  the  boiling  point. 

570.  Franklin's  Experiment. — The  boiling  of 
water  at  a  temperature  below  100°  C.  may  be  shown  as 
follows:  Half  fill  a  Florence  flask  with  water.     Boil  the 
water  until  the  steam  drives  the  air  from  the  upper  part 


430  VAP  OR  12 A  2TO  #. 

of  the  flask.  Cork  tightly,  remove  the  lamp  and  invert 
the  flask.  The  exclusion  of  the  air  may  be  made  more 
certain  by  immersing  the  corked  neck  of  the  flask  in  water 

that  has  been  recently 
boiled.  When  the  lamp 
was  removed,  the  tem- 
perature was  not  above 
100°  C.  By  the  time 
that  the  flask  is  inverted 
and  the  boiling  has 
ceased,  the  temperature 
will  have  fallen  below 
100°  C.  When  the  boil- 
ing stops,  pour  cold 
water  upon  the  flask : 
directly  the  boiling  be- 
F:c.297.  gins  again. 

(a.)  The  cold  water  poured  upon  the  flask  lowers  the  tempera- 
ture of  the  water  in  the  flask  still  further,  but  it  also  condenses 
Borne  of  the  steam  in  the  flask  or  reduces  its  tension  (§  559).  This 
reduction  of  the  tension  lessens  the  work  necessary  to  boiling.  There 
being  enough  heat  in  the  water  to  do  this  lessened  amount  of  work, 
the  water  again  boils  and  increases  the  pressure  until  the  boiling 
point  is  raised  above  the  present  temperature  of  the  water.  The 
flask  may  be  drenched  and  the  water  made  to  boil  a  dozen  times  in 
succession  with  a  single  heating.  The  experiment  may  be  made 
more  striking  by  plunging  the  whole  flask  under  cool  water. 

571.  Papin's  Digester.— At  high  elevations  water  boils  at 
a  temperature  too  low  for  culinary  purposes.  Persons  living  there 
are  obliged  to  boil  meats  and  vegetables  (if  at  all)  in  closed  vessels 
and  under  a  pressure  greater  than  that  of  the  atmosphere.  In  the 
arts,  a  higher  temperature  than  100°  C.  is  sometimes  required  for 
water,  as,  for  example,  in  the  extraction  of  gelatine  from  bones.  In 
a  closed  vessel,  water  may  be  raised  to  a  much  higher  temperature 
than  in  the  open  air,  but,  for  reasons  now  obvious,  water  cannot  be 


VAPORIZATION. 


431 


kept  boiling  in  Such  a  vessel.  Papin's  Digester  Consists  of  a  metal 
vessel  of  great  strength  covered  with  a  lid  pressed  down  by  a 
powerful  screw.  That  the  joint  may  be  more  perfect,  a  ring  of 
sheet  lead  is  placed  between  the  edges  of  the  cover  and  of  the  vessel. 
It  is  provided  with  a  safety  valve,  pressed  close  by  a  loaded  lever. 
When  the  tension  of  the  steam  reaches  a  dangerous  point,  it  opens 
the  valve,  lifting  the  weight  and  thus  allowing  some  of  the  steam 
to  escape. 

(a.)  In  many  cases,  e.  g.,  sugar  refining,  it  is  desirable  to  boil  or 
evaporate  a  liquid  at  as  low  a  temperature  as  possible.  The 
work  is  then  done  in  a  vacuum  pan  from  which  the  vapor  is 
pumped,  the  tension  being  thus  reduced. 


.572.  Marcet's  Globe. — Marcet's  globe  is  represented 
in  Fig.  298.  It  consists  of  a  spherical  metallic  boiler,  five 
or  six  inches  in  diameter,  provided  with  three  openings, 
through  one  of  which  a  thermometer,  T,  passes ;  through 
the  second  of  which  a  glass  manometer  tube,  M,  passes ;  the 
third  opening  being  provided  with  a  stop-cock,  S.  The 
thermometer  and  manometer  tubes  fit  their  openings  so 
closely  that  no  steam  can  escape  at  those  points.  The 
thermometer  bulb  is  exposed  directly  to 
the  steam.  The  lower  end  of  the  manometer 
tube  dips  into  mercury  placed  in  the  lowei 
part  of  the  globe.  The  boiler  is  to  be  half 
filled  with  water  and  heated  until  the 
water  boils,  the  stop-cock  being  open.  As 
long  as  the  stop-cock  is  open,  the  ther- 
mometer will  not  rise  above  100°  C.  When 
the  stop-cock  is  closed,  the  steam  accumu- 
lates, the  pressure  on  the  water  increases, 
the  thermometer  shows  a  rise  of  temperature 
beyond  100°  0.  higher  and  higher  as  the 
FIG  2  s  mercury  rises  in  the  manometer  tube, 


432  VAPORIZATION. 

When  the  mercury  in  the  manometer  tube  is  760  mm. 
above  the  level  of  the  mercury  in  the  boiler,  the  steam 
has  a  tension  of  two  atmospheres,  and  the  thermometer 
will  record  a  temperature  of  about  121°  C. 

573.  Concerning    Steam. — A  given  mass  of 
water  in  the   aeriform,  condition  occupies  nearly 
1700  times  as  much  space   under  a  pressure  of 
one  atmosphere  as  it  does  in  the  liquid  condition. 
In  other  words,  a  cubic  inch  of  water  will  yield  nearly  a 
cubic  foot  of  steam.     Steam   is   invisible.     What  is 
commonly  called  steam  is  not  true  steam,  but  little  globules 
of  water  condensed  by  the  cold  air  and  suspended  in  it. 
By  carefully  noticing  the  steam  issuing  from  the  spout  of 
a  tea-kettle,  it  will  be  observed  that  for  about  an  inch  from 
the  spout   there  is  nothing  visible.      The   steam   there 
has   not  had  opportunity  for  condensation.      The  water 
particles  visible  beyond  this  space  passed  through  it  as 
invisible  steam.      The  steam  in  the  flask  of  Fig.   297  is 
invisible. 

574.  Reference  Tables.— Boiling  Points  under  a  pressure 
of  one  atmosphere : 


Ammonia -40°  C. 

Sulphurous  anhydride. ..—  8 

Ether 35 

Carbon  bisulphide 48 


Alcohol 78°C. 

Water  (pure) 100 

Mercury 350 

Sulphur    447 


Some  solids,  as  iodine,  arsenic  and  camphor  vaporize  without 
risible  intermediate  liquefaction.     The  process  is  called  sublimation 
Boiling  Points  of  water  at  different  pressures : 


Thermometer. 

Barometer. 

Thermometer. 

Atmospheres 

184°  F. 

16.676  inches. 

212°  F. 

1 

190 

18.992 

249.5 

2 

200 

23.454 

2733 

3 

210 

28.744 

318.2 

6 

212 

29.922 

356.6 

10 

215 

81.730             1     415.4 

20 

VAP  ORIZA  TION. 


433 


575.  Definition  of  Boiling  Point.— We  ought 
now  to  be  fully  prepared  to  understand  that  the  boiling 
point  of  a  liquid  is  the  temperature  at  which  it 

gives  off  a  vapor  of  the  same 
tension  as  the  surrounding  at- 
mosphere. 

(a.)  If  there  be  any  doubt  or  lack  of 
comprehension  of  this  proposition,  it  may 
be  removed  by  the  following  experiment : 
A  A  glass  tube,  bent  as  shown  at  A,  has  its 
short  arm  closed  and  its  long  arm  open. 
The  short  arm  is  nearly  filled  with  mer- 
cury, the  space  above  the  mercury  b  ^ing 
filled  with  water.  While  water  is  briskly 
boiling  in  a  flask,  the  bent  tube  is  sus- 
pended in  the  steam,  as  shown  in  Fig. 
299.  Part  of  the  water  in  the  bent  ';ube 
is  changed  to  vapor,  the  mercury  falls  in 
the  short  arm,  and  finally  assumes  the  name 
FIG.  299.  level  in  both  branches. 

576.  Distillation. — Distillation  is   the  process  of 
vaporizing  a  liquid  in  a  heated  vessel  and  subsequently 
condensing  the  vapor  in  a  cool  vessel.     It  is  chiefly  used 
for  the  purpose  of  separating  a  liquid  from  a  solid  which  it 
holds  in  solution,  or  of  separating  a  mixture  of  two  liquids 
having  different  boiling  points.    The  process  depends  upon 
the  fact  that  different  substances  are  vaporized  at  different 
temperatures.      The  apparatus,  called  a  still,  is  made  in 
many  forms,  but  consists  essentially  of  two  parts — the  re- 
tort   for  producing    vaporization,    and   a  condenser    for 
changing  the  vapor  back  to  the  liquid  form.     Fig.  300 
represents  one  form  of  the  apparatus.     It  consists  of  a 
retort,  ab,  the  neck  of  which  is  connected  with  a  spiral 
tube,  dd,  called  the  worm.    The  worm  is  placed  in  a  vessel 
containing  water. 


434 


DISTILLATION. 

ft 


FIG.  300. 

577.  Distillation  of  a  Liquid  from  a  Solid, 

•—  Suppose  that  water  is  to  be  separated  from  the  salt  it 
holds  in  solution.  The  brine  is  placed  in  a  retort  and 
heated  a  little  above  212°  F.  At  this  temperature  the 
water  is  vaporized  while  the  salt  is  not.  The  steam  is 
driven  from  the 
retort  through  the 
worm,  where  it  is 
rapidly  condensed 
and  passes  into  a 
vessel  prepared  to 
receive  it.  The 
salt  remains  in 
the  retort.  Of 
course,  the  water  % 
of  the  vessel  con- 
taining the  worm  FIG.  301. 


totsf ILLATION.  435 

must  be  kept  cool.  This  is  done  by  constantly  feeding  it 
at  the  bottom  with  cold  water,  as  explained  in  the  last 
article. 

(a.)  Fig.  301  represents  a  simpler  form  of  apparatus  for  this  pur 
pose.  The  retort  is  a  Florence  flask,  the  delivery  tube  of  which 
passes  through  a  "water-jacket."  The  method  of  supplying  this 
condenser  with  cold  water  is  evident  from  the  figure.  Sometimes 
the  delivery  tube  passes  directly  into  a  vessel  placed  in  a  cold  water 
bath,  this  vessel  serving  as  both  condenser  and  receiver. 

578.  Distillation  of  a  Liquid  from  a  Liquid. 

— Suppose  that  alcohol  is  to  be  separated  from  water. 
The  solution  is  placed  in  the  retort  and  heated  to  about 
90°  C.,  which  is  above  the  boiling  point  of  alcohol  but 
below  that  of  water.  The  alcohol  will  pass  over  in  a  state 
of  vapor  and  be  condensed,  while  the  water,  etc.,  remains 
behind.  In  practice,  the  alcohol  vapor  passes  over  charged 
with  a  certain  amount  of  steam.  A  receiver  placed  in  a 
bath  containing  boiling  water  is  interposed  between  the 
retort  and  the  worm  or  condenser.  In  this  receiver  the 
steam  condenses,  while  the  vapor  of  alcohol  passes  on  to 
the  worm  where  it  also  is  condensed.  This  process  is  known 
as  "fractional  distillation." 

Recapitulation.—  In  this  section  we  have  considered 
the  meaning  of  Liquefaction  ;  the  Laws  of  Fu- 
sion ;  the  meaning  and  kinds  of  Vaporization  ; 
Evaporation  in  air  and  in  vacuo  ;  Ebullition  and 
its  Laws;  effect  of  Pressure  upon  the  boiling  point; 
Steam  ;  definition  of  Boiling  Point ;  Distilla- 
tion. ; 


436  LATENT  AND  SPECIFIC 


SECTION  HI. 


LATENT    AND    SPECIFIC    HEAT. 

579.  Thermal  Units.— In  §  538  it  was  stated  that 
heat  is  measurable ;  but  that  we  may  measure  it,  a  standard 
or  unit  of  measure  is  necessary.  A  thermal  or  heat 
unit  is  the  amount  of  heat  necessary  to  warm  a 
weight  unit  of  water  one  degree  above  the  freezing 
point.  The  weight  unit  generally  used  is  the  gram, 
kilogram  or  pound;  any  other  weight  unit  may  be  used. 
The  degree  may  be  centigrade  or  Fahrenheit. 

(a.)  We  have  at  least  four  units  in  use.  They  are  the  amounts 
of  heat  necessary  to  warm 

(1.)  A  kilogram  of  water  from  0°  C.  to  1°  C.    (A  calorie.) 
(2.)  A  gram  of  water  from  0°  C.  to  1°  C.    (A  lesser  calorie.) 
(8.)  A  pound  of  water  from  0°  C.  to  1°  C. 
(4.)  A  pound  of  water  from  32°  F.  to  33°  F. 

It  makes  no  practical  difference  which  unit  is  used,  excepting  so 
far  as  convenience  is  concerned,  but  the  unit  must  not  be  changed 
during  any  problem. 

58O.  Two  Fruitful  Questions  —We  have  already  seen 
that  heat  melts  ice,  and  that  during  the  melting  the  temperature  h> 
constant ;  that  heat  boils  water,  and  that  during  the  boiling  the 
temperature  is  constant.  One  feature  of  this  change  of  condition 
remains  to  be  noticed  more  fully.  Take  a  block  of  ice  with  a  tern, 
perature  of  —10°  C.  (14°  F.)  and  warm  it.  A  thermometer  placed  in 
it  rises  to  0°  C.  The  ice  begins  to  melt,  but  the  mercury  no  longei 
rises.  Heat  is  still  applied,  but  there  is  no  increase  of  temperature ; 
the  mercury  in  the  thermometer  remains  stationary  until  the  last 
particle  of  ice  has  been  liquefied.  Then,  and  not  till  then,  does  the 
temperature  begin  to  rise.  It  continues  to  do  so  until  the  ther 
mometer  marks  100°  C.  The  liquid  then  begins  to  boil,  and  the 
temperature  a  second  time  becomes  fixed.  But  during  all  the  time 
that  the  thermometer  stood  at  0°  C.,  or  while  the  ice  was  melting, 
heat  was  given  by  the  lamp  and  received  by  the  ice.  Why  then  did 
not  the  temperature  rise  during  that  time,  instead  of  remaining  the 


LATENT  AND  SPECIFIC  HEAT.  43? 

Bame  until  the  last  particle  of  ice  was  melted?  After  tlie  watel 
began  to  boil,  heat  was  continuously  supplied.  Why  then  was 
there  not  a  continued  increase  of  temperature  ? 

581.  Molecular  Energies.— Heat  is  a  form  of  energy  and 
may  be  kinetic  or  potential.     There  can  be  no  doubt  that  when  a 
body  is  heated  its  molecules  are  thrown  into  violent  motion,  and 
that  as  the  temperature  is  raised  the  energy  of  this  molecular  motion 
is  increased,  or  that  as  this  molecular  motion  is  increased,  the  tern 
perature  is  raised.     But  some  of  this  molecular  energy  that  we  call 
heat,  instead  of  b^ing  used  to  set  the  molecules  of  the  body  in  motion, 
has  work  of  a  different  kind  to  perform.     That  part  of  the  heat 
which  is  spent  in  producing  molecular  vibrations,  which  increases 
the  temperature,  is  called  sensible  heat.     Another  part  is  employed 
in  pushing  the  molecules  of  the  body  asunder,  producing  expansion 
and  change  of  condition.     In  forcing  these  molecules  asunder,  in- 
visible  energy  of  motion  is  changed  to  energy  of  position  as  truly 
and  as  necessarily  as  visible  energy  of  motion  is  changed  to  the 
potential  variety  in  throwing  or  carrying  a  stone  from  the  earth  t« 
the  house-top.    (§  159.) 

582.  Transmutation  of  Molecular  Energy.— In  most 
cases,  but  little  of  the  heat  communicated  to  a  body  is  thus  changed 
to  potential  energy,  the  greater  part  remaining  energy  of  motion 
and  increasing  the  temperature.    But  there  are  certain  crises,  01 
"  critical  occasions,"  on  which  the  greater  part  of  the  heat  communi- 
cated is  transformed  into  energy  of  position.     Thus,  at  the  melting 
point,  a  large  quantity  of  heat  may  be  given  to  ice  without  affecting 
the  temperature  at  all ;  instead  of  raising  the  temperature,  it  merely 
melts  the  ice.    The  energy  used  has  been  changed  from  the  kinetic 
to  the  potential  variety.     In  like  manner,  at  the  boiling  point,  a 
large  quantity  of  heat  may  be  given  to  the  water  without  affecting 
the  temperature  at  all.    Instead  of  raising  the  temperature  further, 
it  merely  vaporizes  the  water,  and  the  steam  has  the  same  tempera- 
ture as  the  water  from  which  it  came.     The  same  change  of  molec- 
ular energy  of  motion  into  molecular  energy  of  position  has  again 
taken  place.     This  heat,  which  is  thus  used  to  overcome  cohesion 
and  change  the  condition  of  matter,  does  not  affect  the  temperature 
and  therefore  is  not  sensible,  but  is  stored  up  as  potential  energy 
and  thus  hidden  or  rendered  latent. 

583.  Definition  of  Latent  Heat.— The  latent 
heat  of  a  substance  is  the  quantity  of  heat  that  is 


438  LATENT  AND  SPECIFIC  HEAT. 

lost  to  thermometric  measurement  during  its 
faction  or  vaporization,  or  the  amount  of  heat  that 
must  be  communicated  to  a  body  to  change  its 
condition  without  changing  its  temperature.  It  may 
be  made  to  reappear  during  the  opposite  changes  after  any 
interval  of  time.  Many  solids  may  undergo  two  changes 
of  condition.  Such  solids  have  a  latent  heat  of  liquefac- 
tion and  a  latent  heat  of  vaporization. 

584.  Latent  Heat  of  Fusion. — We  are  already 
familiar  with  the  fact  that  when  ice  or  any  other  solid  is 
melted  by  the  direct  application  of  heat,  much  of  the  heat 
is  rendered  latent.     In  the  case  of  melting  ice  we  shall 
show  how  this  latent  heat  is  measured,  and  that  its  quan- 
tity is  very  great    We  may  represent  the  process  of  lique- 
faction of  ice  as  follows : 

Water  at  0°  0.  =  ice  at  0"  C.  +  latent  heat  of  water. 

585.  Latent   Heat   of  Solution. — During  the 
process  of  solution,  as  well  as  during  fusion,  heat  is  ren- 
dered latent.    In  either  case  the  performance  of  the  work 
of  liquefaction  demands  an  expenditure  of  kinetic  energy. 
Hence  the  solution  of  a  solid  involves  a  diminution 
of  temperature. 

(a.}  This  loss  may  in  some  cases  be  made  good  by  an  equal  in- 
crease, or  changed  to  gain  by  a  greater  increase  of  sensible  heat 
from  the  chemical  changes  involved  ;  but  in  any  case,  the  act  of 
liquefaction  considered  by  itself  produces  cold.  Thus  a  cup  of 
coffee  is  cooled  by  sweetening  it  with  sugar,  and  a  plate  of  soup  is 
cooled  by  flavoring  it  with  salt. 

586.  Freezing  Mixtures.-—  The  latent  heat  of 
solution  lies  at  the   foundation  of  the   action  of 
freezing  mixtures.    For  example,  when  ice  is  melted 
by  salt,  and  the  water  thus  formed,  in  turn,  dissolves  the 


LATENT  AND  SPECIFIC  HEAT.  439 

salt  itself,  the  double  liquefaction  requires  a  deal  of  heat 
which  is  generally  furnished  by  the  cream  in  the  freezer. 
The  freezing  mixture  most  commonly  used  consists  of  one 
weight  of  salt  and  two  weights  of  snow  or  pounded  ice. 
The  mixture  assumes  a  temperature  of  —18°  0.,  which 
furnished  the  zero  adopted  by  Fahrenheit. 

(a.)  By  mixing,  at  the  freezing  temperature,  three  weights  of 
snow  with  two  weights  of  dilute  sulphuric  acid,  the  temperature 
may  be  reduced  to  about  —20°  F.,  a  diminution  of  over  50  Fahren- 
heit degrees.  If  equal  weights  of  snow  and  dilute  sulphuric  acid 
be  thus  reduced  to  a  temperature  of  —20°  F.  and  then  mixed,  the 
temperature  will  fall  to  about— 60°  F.  By  mixing  equal  weights 
of  sodium  sulphate  crystals  (Glauber's  salt),  ammonium  nitrate  and 
water,  all  at  the  ordinary  temperature,  and  stirring  the  mixture 
with  a  thermometer,  the  temperature  will  be  seen  to  fall  from  about 
65°  F.  to  about  10°  F.,  which  is  considerably  below  the  freezing  point 
of  pure  water.  Glauber's  salt  and  hydrochloric  (muriatic)  acid  form 
a  good  freezing  mixture. 

5S7.  Solidification.  —  Solidification  signifies  the 
passage  from  the  liquid  to  the  solid  condition.  During 
solidification  there  is  an  increase  of  temperature. 
This  may  seem  paradoxical  in  certain  cases,  but,  even  in 
the  case  of  water,  it  is  true  that  solidification  is  a  warming 
process. 

.(#.)  The  sensible  heat  that  disappeared  as  latent  heat  during 
liquefaction,  being  no  longer  employed  in  doing  the  work  of  main- 
taining liquidity,  is  reconverted  into  sensible  heat  and  immediately 
employed  in  increasing  the  molecular  vibrations.  The  molecular 
potential  energy  is  transmuted  into  molecular  kinetic  energy.  This 
is  frequently  illustrated  by  the  precaution  taken  in  winter  to  place 
tubs  of  water  in  vegetable  cellars  that  the  latent  heat  of  the  freez 
Ing  water  may  be  changed  into  sensible  heat  and  thus  protect  the 
vegetables. 

588,    Temperature   of  Solidification.  —  The 

melting  point  is  the  highest  temperature  at  which  solidi- 


440  LATENT  AND  SPECIFIC  HEAT. 

fication  can  take  place,  but  it  is  possible  to  keep  substances 
in  the  liquid  condition  at  lower  temperatures.  Water 
standing  perfectly  quiet  sometimes  cools  several  degrees 
below  the  melting  point  without  freezing,  but,  upon  agita- 
tion in  any  perceptible  degree,  solidification  immediately 
takes  place. 

(a.)  Persons  who  sleep  in  cold  chambers  sometimes  notice,  upon 
arising,  that  as  soon  as  they  touch  a  pitcher  of  water  that  has  been 
standing  in  the  room  over  night,  the  water  quickly  freezes.  If  a 
particle  of  ice  be  dropped  into  the  water  the  same  result  follows. 
We  may  say  that,  in  this  condition,  liquids  have  a  tendency  to  freeze 
which  is  kept  in  check  only  by  the  difficulty  of  making  a  beginning. 

589.  Heat  from  Solidification.— (1.)  By  surrounding, 
with  a  freezing  mixture,  a  small  glass  vessel  containing  water,  and 
a  mercury  thermometer,  the  temperature  of  the  water  may  be  re- 
duced to— 10°  C.  or— 12°  C.  without  freezing  the  water.  A  slight 
movement  of  the  thermometer  in  the  water  starts  the  freezing  and 
the  temperature  quickly  rises  to  0°  C. 

(2.)  Place  a  thermometer  in  a  glass  vessel  containing  water  at 
30°  C.  and  a  second  thermometer  in  a  large  bath  of  mercury  at  —10°  C. 
Immerse  the  glass  vessel  in  the  mercury.  The  temperature  of  the 
water  will  gradually  fall  to  0°C.,  when  the  water  will  begin  to 
freeze  and  its  temperature  become  constant.  In  the  meantime  the 
temperature  of  the  mercury  bath  rises,  and  continues  to  do  so  while 
\he  water  is  freezing. 

(3.)  Dissolve  two  weights  of  Glauber's  salt  in  one  weight  of  hot 
water,  cover  the  solution  with  a  thin  layer  of  oil  and  allow  to  cool, 
in  perfect  quiet,  to  the  temperature  of  the  room.  By  plunging  a 
thermometer  into  the  still  liquid  substance,  solidification  (crystal- 
lization) is  started  and  the  temperature  rapidly  rises.  Dr.  Arnott 
found  that  this  experiment  was  successful  after  keeping  the  solu- 
tion in  the  liquid  condition  for  five  years. 

(4.)  Mix  equal  quantities  of  dilute  sulphuric  acid  and  of  a  satu- 
rated solution  of  calcium  chloride  (not  chloride  of  lime),  the  two 
liquids  having  been  allowed  time  to  acquire  the  temperature  of  the 
room.  The  two  liquids  are  converted  into  solid  calcium  sulphate, 
with  a  marked  increase  of  temperature.  In  this  case,  as  in  some 
of  the  other  cases,  part  of  the  heat  observed  is  probably  due  to 
chemical  action,  but  more  to  the  conversion  of  the  latent  heat  of 
the  liquids. 


LATENT  AND   SPECIFIC  HEAT.  441 

(5.)  To  three  weights  of  quicklime  add  one  weight  of  water 
The  water  will  be  completely  solidified  in  the  slaking  of  the  lime 
with  remarkable  thermal  manifestations.  Carts  containing  quick 
lime  have  been  set  on  fire  by  exposure  to  heavy  rains. 

590.  Change  of  Bulk  during  Solidification. 

— Most  substances  shrink  in  size  during  solidification ;  but 
a  few,  such  as  ice,  cast-iron,  antimony  and  bismuth,  are 
exceptions.  When  melted  cast-iron  is  poured  into  a  mould, 
it  expands  in  solidifying  and  presses  into  every  part  of  the 
mould.  The  tracings  on  the  casting  are,  therefore,  as  clear 
cut  as  they  were  in  the  mould.  A  clear-cut  casting  can 
not  be  obtained  from  lead;  this  is  one  of  the  reasons  why 
antimony  is  made  a  constituent  of  type-metal.  Gold  coins 
have  to  be  stamped ;  they  cannot  be  cast  so  as  to  produce 
a  clear-cut  design.  The  bursting  of  pipes  by  freezing  water 
is  a  common  source  of  annoyance. 

(a.)  An  army  officer  at  Quebec  performed  the  following  experi- 
•»  ment :   He  filled  a  12-inch 

shell  with  water  and  closed 
the  opening  with  a  wooden 
plug  forcibly  driven  in.  The 
shell  was  put  out  of  doors  ; 
the  temperature  being 
—28°  C.,  the  water  froze,  the 
plug  was  thrown  about  300 
feet,  and  a  tongue  of  ice 
about  eight  inches  long  pro- 
truded from  the  opening. 
In  a  similar  experiment,  the 
shell  split  and  a  rim  of  ice 
FIG.  302.  issued  from  the  rent. 

591.  Latent   Heat   of    Vaporization.  —  The 

vaporization  of  a  liquid  is  accompanied  by  the  disappear- 
ance of  a  large  quantity  of  heat,  and  frequently  by  a  diminu- 
tion of  temperature.  There  is  a  change  of  sensible  into 


442  LATENT  AND  SPECIFIC  HEAT. 

latent  heat;  of  kinetic  into  potential  energy.  We 
represent,  for  instance,  the  va- 
porization of  water  as  follows  : 
Steam  at  100°  C.  =  water 
at  100°  C.  {-  latent  heat  of 
steam. 

(a.)  The  cryophorus,  shown  in 
Fig.  254,  consists  of  a  bent  tube 
and  two  bulbs  containing  a  small 
quantity  of  water.  The  air  is  re- 
moved by  briskly  boiling  the  water. 
The  tube  is  sealed  while  the  steam 
is  escaping.  The  instrument  thus 
contains  only  water  and  aqueous 
vapor.  When  the  liquid  is  poured 
into  B,  and  A  is  placed  in  a  freez-  pIG 

ing  mixture,  the  vapor  is  largely 
condensed  in  A  while  more  is  rapidly  formed  in  B.     Crystals  of  ice 
soon  form  on  the  surface  of  the  water  in  B. 

(b.)  Wet  a  block  of  wood  and  place  a  watch  crystal  upon  it.  A 
film  of  water  may  be  seen  under  the  central  part  of  the  glass.  Half 
fill  the  crystal  with  sulphuric  ether  and  rapidly  evaporate  it  by 
blowing  over  its  surface  a  stream  of  air  from  a  small  bellows.  So 
much  heat  is  rendered  latent  in  the  vaporization  that  the  watch 
crystal  is  firmly  frozen  to  the  wooden  block. 

(c.)  Sulphurous  oxide  (SOS)  previously  dried,  is  easily  liquefied 
by  passing  it  through  a  U-tube  immersed  in  a  freezing  mixture. 
When  some  of  this  liquid  is  placed  upon  mercury  in  a  small  capsule 
and  rapidly  evaporated  by  blowing  over  it  a  stream  of  air  from  a 
bellows,  the  mercury  is  frozen  (§  562).  (See  Chemistry,  Exp.  146.) 

592.  Condensation  of  Gases. — Gases  may  be 
condensed  by  union  with  some  liquid  or  solid,  by  cold  or 
by  pressure.  It  has  been  recently  shown  that  any  known 
gas  may  be  liquefied  by  cold  and  pressure.  In  any  case, 
the  condensation  of  a  gas  renders  sensible  a  large 
amount  of  heat. 


LATENT  AND  SPECIFIC  HEAT. 


443 


FIG.  304. 


(a.)  The  change  of  latent  heat  into  sensible  during  the  condensa 
tion  of  a  gas  is  easily  illustrated 
by  the  following  experiment: 
Into  a  gas  bottle,  A,  put  a  tea- 
cup full  of  small  pieces  of  mar- 
ble, and  pour  in  enough  water  to 
cover  them  and  to  seal  the  lower 
end  of  the  thistle  tube.  From 
the  gas  bottle  lead  a  delivery 
tube  to  the  lower  part  of  a  bot- 
tle, B,  containing  a  thermome- 
ter, t.  From  this  bottle  lead  a 
tube  to  the  lower  part  of  the 
bottle  (?,  which  contains  a  ther- 
mometer, T,  with  its  lower  part  embedded  in  a  teacup  full  of  salts 
of  tartar.  Through  the  thistle  tube  of  A  pour  muriatic  acid,  about  a 
thimble-full  at  a  time.  Carbonic  acid  gas  will  be  liberated  and  pass 
through  B  into  C.  There  it  unites  with  the  potassium  carbonate, 
changing  it  to  potassium  bi-carbonate.  In  this  change  from  the 
aeriform  to  the  solid  condition,  the  carbonic  acid  gives  up  all  its 
latent  heat,  as  is  shown  by  the  remarkable  rise  of  the  thermometer 
in  C.  That  this  increase  of  tem  perature  is  not  due  to  the  sensible 
heat  of  a  hot  gas  is  shown  by  the  fact  that  t  is  scarcely  affected 
during  the  experiment, 

(ft.)  When  the  vapor  is  condensed  to  the  liquid  or  solid  form,  the 
heat  previously  rendered  latent  is  given  out  as  sensible  heat  ;  that 
is,  the  energy  of  position  is  changed  back  to  energy  of  motion.  In 
coming  together  again,  the  particles  yield  the  same  amount  of 
kinetic  energy  as  was  consumed  in  their  separation. 

593.  The  Heat  Equivalent  of  the  Fusion  of 
Ice. — If  one  pound  of  water  at  0°  0.  be  mixed  with  one 
pound  of  water  at  80°  C.,  we  shall  have  two  pounds  of  water 
at  40°  C.  But  if  one  pound  of  ice  at  0°  C.  be  mixed  with  one 
pound  of  water  at  80°  C.,  we  shall  have  two  pounds  of  water 
at  0°  0  The  heat  which  might  be  used  to  warm  the  water 
from  0°  to  80°  C..  has  been  used  in  melting  a  like  weight 
of  ice.  Hence,  by  our  definition,  we  see  that  the  latent 
heat  of  one  kilogram  of  water  is  80  calories.  This  means 
that  the  amount  of  heat  required  to  melt  a  quantity 


444  LATENT  AND   SPECIFIC  HEAT. 

of  ice  without  changing  its  temperature  is  eighty 
times  as  great  as  the  heat  required  to  warm  the 
same  quantity  of  water  one  centigrade  degree. 

(a.)  Because  of  this  great  latent  heat  of  water,  the  processes  of 
melting  ice  and  freezing  water  are  necessarily  slow.  Otherwise,  the 
waters  of  our  northern  lakes  might  freeze  to  the  bottom  in  a  single 
night,  while  "  the  hut  of  the  Esquimaux  would  vanish  like  a  house 
in  a  pantomime,"  or  all  the  snows  of  winter  be  melted  in  a  single 
day  with  inundation  and  destruction. 

594.  The  Heat  Equivalent  of  the  Vaporiza- 
tion   of  Water. — Experiment  has  shown  that  the 
amount  of  heat  necessary  to  evaporate  one  weight  unit  of 
water  would  suffice  to  raise  the  temperature  of  537  weight 
units  of  water  1°  C.    Hence,  we  say  that  the  latent  heat  of 
one  kilogram  of  steam  is  537  calories.     This  means  that 
the  amount  of  heat  required  to  evaporate  a  quantity 
of  water  without  changing  its  temperature  is  537 
times  as  great   as  the  heat  required  to  warm  the 
same  quantity  of  water  one  centigrade  degree. 

(a.)  When  a  pound  of  steam  is  condensed,  537  heat  units  (pound  - 
centigrade)  are  liberated.  In  this,  we  see  an  explanation  of  the 
familiar  fact  that  scalding  by  steam  is  so  painfully  severe.  Were 
it  not  for  the  latent  heat  of  steam,  when  water  reached  its  boiling 
point  it  would  instantly  flash  into  steam  with  tremendous  explosion. 

595.  Problems  and  Solutions. — (1.)  How  many  grams 
of  ice  at  0°  C.  can  be  melted  by  1  gram  of  steam  at  100°  C.  ?    One 
gram  of  steam  at  100°  C.,  in  condensing  to  water  at  the  same  tem- 
perature, parts  with  all  its  latent  heat,  or  537  lesser  calories.     The 
gram  of  water  thus   formed    can   give   out  100  more  heat   units. 
Hence,  the  whole  number  of  lesser  calories  given  out  by  the  steam 
in  changing  to  water  at  0°  C.,  the  temperature  at  which  it  can  no 
longer  melt  ice,  is  537  +  100  —  637. 

Let  x  =  the  number  of  grams  of  ice  that  can  be  melted.  Each 
gram  of  ice  melted  will  require  80  lesser  calories.  Hence,  80#  —  the 
number  of  heat  units  necessary.  The  heat  to  melt  the  ice  must 
come  from  the  steam. 

Therefore,  SQx  =  637.  . '.  #  =  7.96  +  grams.     Ans. 


LATENT  AND  SPECIFIC  HEAT.  44<3 

(jj.)  How  many  pounds  of  steam  at  100°  C.  will  just  melt  100 
pounds  of  ice  at  0°  C.  ?  If  x  represent  the  number  of  pounds  of 
steam  required,  that  quantity  of  steam  at  100°  C.  will  furnish.  637a- 
heat  units.  To  melt  100  Ibs.  of  ice,  (80  x  100  =)  8,000  heat  units 
will  be  required. 

Hence,  637»  '=  8,000.  .'.   x  =  12.55  +  Ibs.    Am. 

(3.)  What  weight  of  steam  at  100°  C.  would  be  required  to  raise 
500  pounds  of  water  from  0°  C.  to  10°  C.  ? 
Let  x  =  the  number  of  pounds  of  steam  required. 
(537  +  90)z  =  500  x  10.  .'.  x  =  7.97  +  Ibs.    Ans. 

(4.)  If  4  Ibs.  of  steam  at  100  C.  be  mixed  with  200  Ibs.  of  water  at 
10°  C.,  what  will  be  the  temperature  of  the  water  ? 

Let  x  —  the  temperature.  In  condensing  to  water  at  100°  C.,  the 
4  Ibs.  of  steam  will  give  out  (537  x  4  =)  2,148  heat  units.  This 
4  Ibs.  of  water  will  then  give  out  4(100  —  x)  heat  units.  Hence,  the 
steam  will  impart  2,148  +  4(100  —  x)  heat  units.  The  200  Ibs.  of 
water  in  rising  from  10°  C.  to  x°  will  absorb  200(#  —  10)  heat  units. 

Hence,  2,148  +  4(100 -x)  =  200(#-10).      .'.  x  =  22.29° C.    Ana. 

596.  Illustration  of  Specific  Heat. —When 
the  temperature  of  a  body  changes  from  30°  to  20°,  the 
body  loses  just  as  much  heat  as  it  gained  in  passing  from 
20°  to  30°.  This  heat  lost  by  a  cooling  body  may  be 
measured,  like  any  other  energy,  by  the  work  it  can  per- 
form. If  equal  weights  of  different  bodies  be  raised  to  the 
same  temperature,  the  amount  of  ice  that  each  can  melt 
will  be  proportional  to  the  number  of  thermal  units  they 
severally  contain.  A  pound  of  sulphur  at  212°  F.  will 
melt  £  as  much  ice  as  a  pound  of  boiling  water.  Hence, 
it  required  only  |  as  much  heat  to  heat  the  sulphur  from 
the  freezing  point  to  212°  F.,  as  it  did  to  heat  the  water 
to  the  same  temperature;  in  scientific  phraseology,  the 
specific  heat  of  sulphur  is  £. 

(a.)  In  an  experiment  of  this  kind,  if  the  cooling  substance  change 
its  condition,  the  latent  heat  set  free  as  sensible  heat  must  be  taken 
into  account.  Special  precaution  must  also  be  taken  in  measuring 


446 


LATENT  AND   SPECIFIC  HEAT. 


the    heat    expended,    to    avoid  melting  of  the   ice   by  the  heal 

of  the  surrounding  air  and  making  proper 

allowance  for  the  heat  expended  in  warming 

the  apparatus  itself.    Fig.  256  represents  a 

form  of  calorimeter  frequently  used  in  such 

Bxperiments.     M  contains  the  heated  body 

whose  weight  and  temperature  are  known. 

A  contains  the  ice  to  be  melted,  the  liquid 

thus  produced  escaping  by  D.    B  is  an  ice 

jacket  to  prevent  melting  of  the  ice  in  A  by 

the  heat  of  the  air. 


597.  Definition  of  Specific 
Heat. — The  specific  heat  of  a  body 
is  the  ratio  between  the  quantity 


FIG.  305. 


of  heat  required  to  warm  that  body  one  degree  and 
the  quantity  of  heat  required  to  "warm  an  equal 
weight  of  water  one  degree. 

(a.)  It  is  very  important  to  bear  in  mind  that  specific  heat,  like 
specific  gravity,  is  a  ratio  ;  nothing  more  nor  less.  The  specific  heat 
of  water,  the  standard,  is  unity.  This  ratio  will  be  the  same  for 
any  given  substance,  whatever  the  thermal  unit  or  thermometric 
scale  adopted. 

598.  Specific  Heat  Determined  by  Mixture. 

— One  of  the  simplest  methods  of  measuring  specific  heat 
is  by  mixture.  Suppose,  e.  g.,  that  3  kilograms  of  mercury 
at  100°  C.  are  mixed  with  1  kilogram  of  ice-cold  water  and 
that  the  temperature  of  the  mixture  is  9°  C.  How  shall 
we  find  the  specific  heat  of  mercury  ? 

Let  x  =  the  specific  heat  of  the  mercury,  or  the  amount  of  heat 
lost  by  one  kilogram  of  mercury  for  each  degree  of  change  of 
temperature.  Then  will 

3.r  =  the  number  of  heat  units  lost  by  the  given  amount  of  mer- 
cury for  every  degree  of  change  of  temperature,  and  91  times 
3x,  or 

273x  =  the  number  of  heat  units  lost  by  the  mercury  in  passing 
from  100°  to  9°  C. 

The  specific  heat  of  water  is  1.  This  multiplied  by  the  number 
•f  kilograms  of  water  taken  is  1,  which  represents  the  number  of 


LATENT  AND  SPECIFIC  HEAT. 


447 


heat  units  gained  by  that  quantity  of  water  for  each  degree  of 
change  of  temperature.  Then  will  9  represent  the  number  of  heat 
units  gained  by  the  water  in  passing  from  0°  to  9°.  But  no  heat 
has  been  destroyed  or  wasted  ;  what  the  mercury  has  lost,  the  water 
has  gained. 

Mercury.  Water. 

Specificheat x  1 

Weights  taken 3  1 

No.  of  degrees  of  change 91  9 

Heat  units 273$    =    9 

.'.    x  —  .033,  the  specific  heat  of  mercury. 

599.  Heated  Balls  Melting  Wax.— The  differ- 
ence  between  bodies  in  respect  to  specific  heat  may  be 
roughly  illustrated  as  follows :  small  balls  of  equal  weight, 
made  severally  of  iron,  copper,  tin,  lead  and  bismuth  are 
heated  to  a  temperature  of  180°  or  200°  C.  by  immersing 
them  in  hot  oil  until  they  all  acquire  the  temperature  of 
the  oil.    They  are  then  placed  on  a  cake  of  beeswax  about 

half  an  inch 
thick.  The  iron 
and  copper  will 
melt  their  way 
through  the 
wax,  the  tin  will 
nearly  do  so, 
while  the  lead 
and  bismuth 
sink  not  more  than  half  way  through  the  wax. 

600.  Reference  Tables.— (1.)  Specific  Heat  of  some  sub- 
stances : 

Iron...  .1138 


FIG.  306. 


Hydrogen 3.4090 

Water 1.0000 

Ammonia  (gas) 5084 

Air 2375 

Oxygen 2175 

Sulphur 2026 

Diamond 1469 


Copper. 0952 

Silver 0570 

Tin   0562 

Mercury 0333 

Lead 0314 

Bismuth 0308 


448  LATENT  AND  SPECIFIC  HEAT. 

(2.)  Specific  heat  of  some  substances  in  different  states  : 

Solid.  Liquid.  Aeriform 

Water 5050  1.0000  .4805 

Bromine 0843  .1060  .0555 

Alcohol .6050  .4534 

Ether .5467  .4797 

6O1.  Specific  Heat  of  Water.—  Water  in  iU 
liquid  form  has  a  higher  specific  heat  than  any 
other  substance  except  hydrogen.  For  this  reason  the 
ocean  and  our  lakes  are  cooled  and  heated  more  slowly 
than  the  land  and  atmosphere.  They  thus  modify  sudden 
changes  of  temperature,  and  give  rise  to  the  well  known 
fact  that  the  climate  of  the  sea-coast  is  warmer  in  wintei 
and  cooler  in  summer  than  that  of  inland  places  of  the 
same  latitude.  The  heat  of  summer  is  stored  up  in  the 
ocean  and  slowly  given  out  during  the  winter.  This  fact 
also  explains  a  phenomenon  familiar  to  those  living  on  the 
borders  of  the  ocean  or  great  lakes.  Because  of  its  lower 
specific  heat,  the  land  becomes  during  the  day  more  heated 
than  the  water.  The  air  in  contact  with  the  land  thus 
becomes  more  heated,  expands,  rises  and  forms  an  upper 
current  from  the  land  accompanied  by  a  corresponding 
under  current  to  the  land,  the  latter  constituting  the 
welcome  sea  or  lake  breezes  of  summer.  After  sunset, 
however,  the  land  cools  more  rapidly  than  the  water,  the 
process  is  reversed,  and  we  have  an  under  current  from 
the  land  constituting  the  land  breeze. 

EXERCISES. 

1.  One  kilogram  of  water  at  40°  C.,  2  kilograms  at  30°  C.,  3  kilo- 
grams at  20°  C.,  and  4  kilograms  at  10°  C.  are  mixed.     Find  the  tern 
perature  of  the  mixture.  Am.  20°  C. 

2.  One  pound  of  mercury  at  20°  C.  was  mixed  with  one  pound  ol 


LATENT  AND   SPECIFIC  HEAT.  449 

water  at  0°  C.,  and  the  temperature  of  the  mixture  was  0.634°  C. 
Calculate  the  specific  heat  of  mercury. 

3.  What  weight  of  water  at  85°  C.  will  just  melt  15  pounds  of 
ice  at  0°  C.  ?  Ans.  14.117  Ib. 

4.  What  weight  of  water  at  95°  C.  will  just  melt  10  pounds  of  ice 
at  —10°  C.  ?  Ana.  8.947  Ib. 

5.  What  weight  of  steam  at  125°  C.  will  .melt  5  pounds  of  ice  at 
—8°  C.  and  warm  the  water  to  25°  C.  ?  Ans.  0.87  Ib. 

6.  How  much  mercury  could  be  warmed  from  10°  C.  to  20°  C.  by 
1  kilogram  of  steam  at  200°  C.  ?  Ans.  1997  Kg. 

7.  Equal  masses  of  ice  at  0°  C.  and  hot  water  are  mixed.     The  ice 
is  melted  and  the  temperature  of  the  mixture  is  0°  C.     What  was 
the  temperature  of  the  water  ?  Ans.  80°  C. 

8.  Ice  at  0°  C.  is  mixed  with  ten  times  its  weight  of  water  at 
20°  C.    Find  the  temperature  of  the  mixture.     Ans.  11°  C.  nearly. 

9.  One  pound  of  ice  at  0°  C.  is  placed  in  5  pounds  of  water  at 
12°  C.     What  will  be  the  result? 

10.  Find  the  temperature  obtained  by  condensing  10  g.  of  steam 
at  100°  C.  in  1  Kg.  of  water  at  0°  C.  Ans.  6.3°  C. 

11.  A  gram  of  steam  at  100°  C.  is  condensed  in  10  grams  of  water 
at  0°  C.     Find  the  resulting  temperature.  Ans.  58°  C.  nearly. 

12.  If  200  g.  of  iron  at  300°  C.  be  plunged  into  1  Kg.  of  water  at 
0°  C.,  what  will  be  the  resulting  temperature  ?  Ans.  6.67°  C. 

13.  Find  the  specific  heat  of  a  substance,  80  g.  of  which  at  100°  C. 
being  immersed  in  200  g.  of  water  at  10°  gives  a  temperature  of 
20°  C. 

14.  If  300  g.  of  copper  at  100°  C.  be  immersed  in  700  g.  of  alcohol 
at  0°  C.,  what  will  be  the  resulting  temperature  ?    (§  600.) 

15.  What  will  be  the  result  of  mixing  5  ounces  of  snow  at  0°  C. 
with  23  ounces  of  water  at  20°  C.  ? 

16.  A  pound  of  wet  snow  mixed  with  5  pounds  of  water  at  20°  C. 
yields  6  pounds  of  water  at  10°  C.     Find  the  proportions  of  snow 
and  water  in  the  wet  snow. 

17.  What  weight  of  mercury  at  0°  C.  will  be  raised  one  degree 
by  dropping  into  it  150  g.  of  lead  at  300°  C.  ? 

18.  Find  the  result  of  mixing  6  pounds  of  snow  at  0°  C.  with 
7  pounds  of  water  at  50°  C. 

Recapitulation. — In  this  section  we  have  considered 
the  definition  of  Thermal  Units ;  two  Varieties 
of  Molecular  Energy  ;  their  mutual  Converti- 
bility ;  the  definition  of  Latent  Heat ;  the  latent 


450  MODES   OF  DIFFUSING   HEAT. 

heat  of  Fusion  and  of  Solution  ;  Freezing  Mix- 
tures ;  Solidification,  and  the  Temperature  of 
Solidification ;  Heat  from  Solidification ; 
Change  of  Bulk  during  solidifying;  the  Latent 
Heat  of  Vaporization  ;  the  Condensation  of 
Gases ;  the  Latent  Heat  of  Water  and  of 
Steam;  illustration  and  definition  of  Specific  Heat; 
specific  heat  Determined  by  Mixture;  specific 
heat  Determined  by  Melting  Wax;  tables  of 
specific  heat,  and  the  Specific  Heat  of  Water. 


IV, 


\. 
MODES    OF    DIFFUSING    HEAT. 

602.  Diffusion  of  Heat.—  Heat  is  diffused  in  three  ways  . 
Dy  conduction,  convection,  and  radiation.     Whatever  the  mode  of 
diffusion,  there  is  a  tendency  to  produce  uniformity  of  temperature. 

603.  Conduction.  —  If  one  end  of  an  iron  poker  be 
thrust  into  the  fire,  the  other  end  will  soon  become  too 
warm  to  be  handled.    It  has  been  heated  by  conduction, 
the  molecules  first  heated  giving  some  of  their  heat  to  those 
adjacent,  and  these  passing  it  on  to  those  beyond.     There 
was  a  transfer  of  motion  from  molecule  to  molecule.     The 
process  by  which  heat  thus  passes  from  the  hotter 
to  the  colder  parts  of  a  body  is  called  conduction 
of  heat.    The  propagation  is  very  gradual,  and  as  rapid 
through  a  crooked  as  through  a  straight  bar. 

604.  Differences  in  Conductivity.—  If,  instead 
of  an  iron  poker,  we  use  a  glass  rod  or  wooden  stick,  the 
end  of  the  rofl  may  be  melted  or  the  end  of  the  stick 


MODES   OF  DIFFUSING   HEAT. 


451 


FIG.  307- 

burned  without  rendering  the  other  end  uncomfortably 
warm.  We  thus  see  that  some  substances  are  good  con- 
ductors of  heat  while  some  are  not.  Thrust  a  silver  and 
a  German  silver  spoon  into  the  same  vessel  of  hot  water, 
and  the  handle  of  the  former  will  become  much  hotter 
than  that  of  the  latter. 

(a.)  Fig.  307  represents  a  bar  of  iron  and  one  of  copper  placed 
end  to  end  so  as  to  be  heated  equally  by  the  flame  of  the  lamp. 
Small  balls  (or  nails)  are  fastened  by  wax  to  the  under  surfaces  of 
the  bars  at  equal  distances  apart.  More  balls  can  be  melted  from 
the  copper  than  from  the  iron.  The  number  of  balls  melted  off,  not 
the  rapidity  with  which  they  fall,  is  the  test  of  conductivity.  The 
rapidity  would  depend  more  upon  specific  heat. 

(&.)  Relative  thermal  conductivity  of  some  metals : 

Silver 100 

Copper 74 

Gold 53 

Brass 24 

Tin...  15 


Iron 12 

Lead 9 

Platinum 8 

German  silver 6 

Bismuth  .  , 2 


The  above-named  metals  arrange  themselves  in  the  same  order 
with  reference  to  the  conduction  of  electricity,  silver  being  the  best 
and  bismuth  the  poorest.  This  relation  suggests  a  similarity  of 
nature  between  these  two  agents. 

OO5.  Conductivity  of  Fluids. — Liquids  and 
aeriform  bodies  are  poor  conductors  of  Jieat.  The 
surface  of  a  liquid  may  be  intensely  heated  without  sensibly 
effecting  the  temperature  an  inch  below. 


452 


MODES  OF  DIFFUSING  HEAT. 


FIG. 


Cork  the  neck  of  a  glass  funnel  and  pass  the  tube  of  an 
inverted  thermometer  through  the  cork,  or  use  an  air 
thermometer,  as  shown  in  the  figure.  Cover  the  ther- 
mometer bulb  to  the  depth  of  about  half  an  inch  with 
water.  Upon  the  water  pour  a  little  sulphuric  ether 
and  ignite  it.  The  heat  of  the  flame  will  be  intense 
enough  to  boil  a  small  quantity  of  water  held  over  it> 
but  the  thermometer  below  will  be  scarcely  affected. 
Fasten  a  piece  of  ice  at  the  bottom  of  a  glass  tube, 
and  cover  it  to  the  depth  of  several  inches  with  water. 
Hold  the  tube  at  an  angle  of  about  45°,  and  apply  the 
flame  of  a  lamp  below  the  upper  part  of  the  water. 
The  water  there  may  be  made  to  boil  without  melting 
the  ice.  The  conductivity  of  gases  is  probably  lower 

308.    than  that  of  liquids. 


6O6.  Convection. — Fluids  (with  the  exception  of 
mercury,  which  is  a  metal)  being  poor  conductors,  they 
cannot  be  heated  as  solids  gen- 
erally are.  Water,  e.g.,  must  be 
heated  from  below;  the  heated 
molecules  expand  and  rise  while 
the  cooler  ones  descend  to  take 
their  place  at  the  source  of  heat. 
These  currents  in  heating  water 
may  be  made  visible  by  dropping 
a  small  quantity  of  cochineal  or 
oak  sawdust  into  the  vessel  con- 
taining the  water.  This  method 
of  diffusing  heat,  by  actual 
motion  of  heated  fluid  masses, 
is  called  convection.  Expansion 
by  heat  and  the  force  of  gravity  are  essential  to  convection. 
Since  aeriform  bodies  are  expanded  more  by  heat  than 
liquids  are,  these  currents  of  heated  gases  are  more  active 
than  those  of  liquids.  Hence  the  drafts  of  lamps  and 
stoves,  the  existence  of  trade  winds,  etc. 


FIG.  309. 


MODES  OF  DIFFUSING  BEAT.  453 

6O7.  The  Third  Mode  of  Heat  Diffusion.— When  a 

hand  is  held  over  a  heated  stove,  heat  is  carried  to  the  hand  by  con- 
vection and  given  up  to  the  hand  by  conduction.  But  when  the 
hand  is  held  before  the  stove  it  is  also  heated,  not  by  conduction,  for 
fluids  have  little  conducting  power  ;  not  by  convection,  for  convec- 
tion currents  are  ascending.  How  then  does  the  heat  get  to  the 
hand  ?  The  query  comes  to  us  with  still  greater  force  when  we 
consider  the  transmission  of  the  sun's  heat  to  the  earth,  for  the 
atmosphere  can  carry  it  by  neither  conduction  nor  convection. 
More  important  yet,  how  does  the  sun's  heat  reach  the  earth's 
atmosphere  ?  This  heat  passes  through  the  atmosphere  without 
heating  it.  If  along  a  poker  thrust  into  the  fire  the  hand  be  moved 
toward  the  stove,  the  temperature  increases.  If  a  person  ascend 
through  the  atmosphere  toward  the  sun  the  temperature  diminishes. 
We  have  here  a  wholly  new  set  of  thermal  phenomena,  heat  pass- 
ing through  a  substance  and  leaving  the  condition  of  that  substance 
unchanged. 

6O8.  Lumiiiiferous  Ether. — In  the  case  of  actual, 
mechanical  energy,  the  rapid  motion  of  bodies,  e.  g.,  a 
vibrating  guitar  string,  is  partly  carried  off  by  the  air  in 
the  shape  of  sound.  When  the  sound  reaches  the  auditory 
nerve  it  represents  a  certain  amount  of  mechanical  energy 
of  motion  which  has  been  carried  from  the  string  by  the 
air.  There  is  sufficient  reason  for  believing  that 
there  is  a  medium  pervading  all  space  which  car- 
ries off  part  of  the  invisible  motions  of  molecules, 
just  as  the  air  carries  off  a  portion  of  the  motion 
of  moving  masses.  This  medium,  called  the  luminiferous 
ether,  occupies  all  space.  The  gaps  between  the  sun,  the 
planets  and  their  satellites  are  filled  with  this  ether.  "  It 
makes  the  universe  a  whole  and  renders  possible  the  inter- 
communication of  light  and  energy  between  star  and  star." 

OO9.  Density  and  Elasticity  of  the  Ether.— This  ether 
is  wonderful,  not  only  in  its  incomprehensible  vastness  but  equally 
so  in  its  subtleness.  While  it  surrounds  the  suns  of  unnumbered 
systems  and  fills  all  interstellar  space,  it  also  surrounds  the  smallest 


454  MODES  OF  DIFFUSING 


particles  of  matter  and  fills  intennolecular  space  as  well.  It  is 
called  luminiferous  because  it  is  tlie  medium  by  which  light  ia 
propagated,  it  serving  as  a  common  carrier  for  both  heat  and  light. 
We  have  seen  (§  426)  that  the  velocity  of  sound  depends  upon  two 
considerations,  the  elasticity  and  the  density  of  the  medium.  The 
enormous  velocity  with  which  the  ether  transmits  heat  and  light  as 
wave  motion  (about  186,000  miles  per  second),  compels  us  to  assume 
for  the  ether  both  extreme  elasticity  and  extreme  tenuity. 

610.  Radiant  Heat.  —  We  have  seen  that  the  mole- 
cules of  a  heated  body  are  in  a  state  of  active  vibration. 
The  motion  of  these  vibrating  molecules  is  communicated 
to  the  ether  and  transmitted  by  it,  as  waves,  with  wonder- 
ful velocity.    Thus,  when  you  hold  your  hand  before  a  fire, 
the  warmth  that  you  feel  is  due  to  the  impact  of  these 
ether-  waves  upon  your  skin  ;  they  throw  the  nerves  into 
motion,  just  as  sound-waves  excite  the  auditory  nerve,  and 
the  consciousness  corresponding  to  this  motion  is  what  we 
popularly  call  warmth.     Heat  thus  propagated  by  the 
ether,  instead  of  by  ordinary  forms  of  matter,  is 
Radiant  Heat.    Tlie  process  of  propagation 

is  called  radiation.  t 

611.  The  Transmission  through  a 
Vacuum.  —  Radiant  heat  mill  traverse  a 
vacuum.    "We  might  infer  this  from  the  fact 
that  the  sun  radiates  heat  to  the  earth.    It  may 
be  also  shown  experimentally. 

(a.)  A  thermometer  is  sealed  air-tight  in  the  bottom 
of  a  glass  globe  in  such  a  way  that  the  bulb  is  near  the 
centre  of  the  globe.     The  neck  of  the  flask  is  to  be     pjGi  310. 
about  a  yard  long.     The  apparatus  being  filled  with 
mercury  and  inverted  over  a  mercury  bath,  a  Torricellian  vacuum 
is  formed  in  the  globe  and  upper  part  of  the  tube.     The  tube  is 
then  melted  off  above  the  mercury.     When  the  globe  is  immersed 
In  hot  water,  the  thermometer  immediately  indicates  a  rise  of  tern 


MODES  OF  DIFFUSING  HEAT.  455 

perature.  There  is  no  chance  for  convection ;  conduction  acts  much 
more  slowly. 

612.  Rectilinear  Propagation. — Radiant  heat 
travels    in    straight    lines    through    any    uniform 
medium. 

(a.)  Between  any  source  of  heat  and  a  thermometer  place  several 
screens.  If  holes  be  made  in  the  screens  (See  Fig.  321)  so  that  a 
straight  line  from  the  source  of  heat  to  the  thermometer  may  pass 
through  them,  the  thermometer  will  be  affected  by  the  heat.  By 
moving  one  of  the  screens  so  that  its  opening  is  at  one  side  of  this 
line,  the  heat  is  excluded.  In  a  very  warm  day  a  person  may  step 
from  a  sunny  into  a  shady  place  for  the  same  reason.  The  heat  that 
moves  along  a  single  line  is  called  a  ray  of  heat. 

613.  Radiation  Equal  in  all  Directions. — 

Heat  is  radiated  equally  in  all  directions.  If  an 
iron  sphere  or  a  kettle  of  water  be  heated,  and  delicate 
thermometers  placed  on  different  sides  of  it  at  equal  dis- 
tances, they  will  all  indicate  the  same  temperature. 

614.  Radiation  Depends   upon   Tempera- 
ture  of  the   Source. — The  intensity  of  radiant 
heat    is    proportional    to    the    temperature    of  the 
source. 

(a.)  Near  a  differential  thermometer,  place  a  vessel  of  water  10° 
warmer  than  the  temperature  of  the  room.  Notice  the  effect  upon 
the  thermometer.  Heat  the  water  10°  more  and  repeat  the  experi- 
ment at  the  same  distance.  Then  heat  the  water  10°  still  more  and 
repeat  the  experiment  again.  The  effects  upon  the  thermometer  will 
be  as  the  numbers  one,  two  and  three. 

615.  Effect   of  Distance.— The   intensity  of 
radiant  heat  varies  inversely  as  the  square  of  the 
distance. 

(a.)  Place  the  differential  thermometer  at  a  certain  distance  from 
the  heated  water  and  note  the  effect.  Removing  the  thermometei 
to  twice  that  distance  the  effect  is  only  one-fourth  as  great,  etc. 


456  MODES  OF  DIFFUSING  HEAT. 

616.  Incident   Rays.— When    radiant   heat   falls 
upon  a  surface  it  may  be  transmitted,  absorbed  or  reflected, 
ff  transmitted,  it  may  be  refracted.    Kock   salt  crystal 
transmits  nearly  all,  reflects  very  little,  and  absorbs  hardly 
any.    Lampblack  absorbs  nearly  all,  reflects  very  little,  and 
transmits  none.    Polished  silver  reflects  nearly  all,  absorbs 
a  little,  and  transmits  none. 

617.  Diathermancy. — Bodies  that  transmit  ra- 
diant heat  freely  are  called  diathermanous;  those 
that  do  not  are  called  atherrnanous.    These  terms 
are  to  heat,  what  transparent  and  opaque  are  to  light. 
Rock  salt  is  the  most  diathermanous  substance  known. 
Heat  that  is  radiated  from  a  non-luminous  source,  as  from 
a  ball  heated  below  redness,  is  called  obscure  heat ;  while 
part  of  that  radiated  from  a  luminous  source,  as  from  the 
sun  or  from  a  ball  heated  to  redness,  is  called  luminous 
heat.    Heat  from  a  luminous  source  is  generally  composed 
of  both  luminous  and  obscure  rays. 

618.  Selective  Absorption. — The  power  of  any 
given  substance  to  transmit  heat  varies  with  the  nature  of 
the  heat  or  of  its  source.     For  example,  glass,  water  or 
alum  allows  the  sun's  luminous  heat  rays  to  pass,  while 
absorbing  nearly  all  of  the  heat  rays  from  a  vessel  filled 
with  boiling  water.    In  other  words,  these  substances  are 
diathermanous  for  luminous  rays,  but  athermanous  for 
obscure  rays.    The  physical  difference  between  luminous 
and  obscure  heat  rays  will  subsequently  be  explained. 

(a.)  A  solution  of  iodine  in  carbon  di-sulphide  transmits  obscure 
rays  but  absorbs  luminous  rays.  By  means  of  these  substances, 
luminous  and  obscure  rays  may  be  sifted  or  separated  from  each 
other.  Dry  air  is  highly  diathermanous  ;  watery  vapor  is  highly 
athermanous  for  obscure  rays. 


REFLECTION  Of  SEAT.  457 

619.  Reflection  of  Heat.— When  radiant  heat 
falls  upon  an  athermanous  body,  part  of  it  is  generally 
absorbed  and  raises  the  temperature  of  the  body.  The 
rest  is  reflected,  the  energy  still  existing  in  the  ether  waves. 
The  angle  of  incidence  equals  the  angle  of  reflec- 
tion (§  97). 


FIG.  311. 

(a.)  In  Fig.  311,  the  source  of  heat  at  A  is  a  Leslie's  cube  filled  with 
hot  water.  S  is  an  athermanous  screen  with  an  aperture  for  the 
passage  of  rays  from  A  to  the  reflector  B.  The  line  CB  is  per- 
pendicular to  the  reflector.  When  D,  the  bulb  of  the  differential 
thermometer,  is  placed  so  that  the  angle  ABC  equals  the  angle 
DBG,  the  reflected  rays  will  strike  the  bulb  and  raise  the  temper- 
ature. 

62O.  Reflection  by  Concave  Mirrors. — By  the 

use  of  spherical  or  parabolic  mirrors,  remarkable  heating 
effects  may  be  produced.  When  parallel  rays  (like  the 
sun's  rays)  strike  directly  upon  such  a  mirror,  they  are 
reflected  to  a  focus.  Any  easily  combustible  substance 
held  at  the  focus  may  be  thus  ignited. 

(a.)  Two  such  mirrors  may  be  placed  as  shown  in  Fig.  312.  At 
the  focus  of  one  reflector  place  a  hot  iron  ball  ;  at  the  focus  of  the 
other,  a  bit  of  phosphorus  or  gun-cotton.  If  the  apparatus  be 
arranged  with  exactness,  the  combustible  will  be  quickly  ignited. 


458 


HEFRACTlON  OF  BEAf. 


FIG.  312. 

Replace  the  iron  ball  with  a  Leslie's  cube  containing  hot  water ; 
at  the  focus  of  the  other  reflector  place  one  bulb  of  the  differential 
thermometer.  The  rise  of  temperature  at  this  focus  will  be  clearly 
shown,  even  when  the  other  bulb  is  nearer  the  source  of  heat  than  the 
focus  is. 

621.  Refraction  of  Heat.— When  rays  of  heat 
fall  obliquely  upon  a  diathermanous  body,  they  will  be 
bent  from  a  straight  line  on  entering  and  leaving  the  body. 
This  bending  of  the  ray  is  called  refraction.  Many 
rays  of  heat  may  thus  be  concentrated  at  a  focus,  as  in  the 
case  of  a  common  burning-glass.  By  the  aid  of  a  spectacle- 
glass,  the  sun's  rays  may  be  made  to  ignite  easily  combus- 
tible substances.  The  refraction  of  obscure  rays  cannot 
be  shown  by  a  glass  lens,  since  glass  is  athermanous  for 
such  rays.  But  if  a  rock-salt  lens  be  held  before  a  source 
of  obscure  heat,  and  the  face  of  a  thermopile  placed  at 


RADIANT  BEAT.  450 

the  focus  of  the  lens,  the  galvanometer  needle  will  at  once 
turn  aside,  showing  a  rise  of  temperature.  If  the  face  of 
the  pile  be  placed  anywhere  else  than  at  the  focus,  there 
vill  be  no  such  deflection  of  the  needle. 

622.  Change  of  Radiant  into  Sensible  Heat, 

-  -Of  all  the  rays  falling  upon  any  substance,  only  those 
ihat  are  absorbed  are  of  effect  in  heating  the  body  upon 
which  they  fall.  The  motion  of  the  ether  waves  may  be 
changed  into  vibrations  of  molecules  of  ordinary  matter, 
and  thus  produce  sensible  heat,  but  the  same  energy  can- 
not exist  in  waves  of  ether  and  in  ordinary  molecular 
vibrations  at  the  same  time. 

(a.)  Phosphorus  or  gun-cotton  may  be  ignited  by  solar  rays  at 
the  focus  of  a  lens  made  of  clear  ice.  The  heat  rays  pass  through 
the  ice  without  melting  it.  It  is  only  when  the  radiation  is  stopped 
that  the  energy  of  the  ray  can  warm  anything. 

623.  Determination  of  Absorbing',  Reflecting  and 
Radiating1    Powers.— For    experiments    in    determining   the 
absorbing,  reflecting  and  radiating  powers  of  solids,  the  apparatus 
generally  used  consists  of    a    Leslie's  cube,   concave  mirrors   of 
different  materials,  and  a  differential  thermometer  or  a  thermopile. 
The  Leslie's  cube  is  a  box  about  three  inches  on  each  edge,  the 
sides  being  made  of,  or  covered  with,  different  materials,  to  show 
their  differences  in  radiating  power.     The  cube  filled  with  hot  water 
is  placed  before  the  reflector,  and  a  bulb  of  the  thermometer  is 
placed  at  the  focus.     By  turning  different  faces  of  the  cube  toward 
the  mirror,  the  relative  radiating  powers  are  determined.    By  using 
different  mirrors,  the  reflecting  powers  are  determined.     By  coating 
the   bulb  with   different   substances,  their  absorbing  powers  are 
determined.      The  relative   radiating  powers   of  several  common 
substances  are  as  given  below : 


Lampblack 100 

Paper 98 

Crown  glass 90 


Tarnished  lead. 45 

Mercury 20 

Gold,  silver,  copper 12 


624.   Mutual  Relations  of  Absorption,  Re- 
flection and  Radiation. — By  means  like  those  men- 


460  RADIANT  HEAT. 

tioned  in  the  last  paragraph,  it  has  been  shown  that 
good  absorbents  are  good  radiators  and  poor  re- 
flectors, and  vice  versa ;  that  the  radiating  power  of  a 
body  depends  largely  upon  the  nature  of  its  surface  ;  that 
smoothing  and  polishing  the  surface  increases  reflecting 
power,  and  diminishes  absorbing  and  radiating  power; 
that  roughening  and  tarnishing  the  surface  increases  the 
absorbing  and  radiating  powers,  and  diminishes  the  re- 
flecting power.  The  poivers  of  absorption  and  radi- 
ation go  hand  in  hand.  (See  §§  721,  722.) 

(a.)  Make  a  thick  paint  of  a  teaspoonful  of  lampblack  and  & 
little  kerosene  oil.  With  this,  paint  the  right-hand  face  of  the 
left-hand  bulb  (tin  can  of  the  differential  thermometer  described  in 
Appendix  R).  Provide  another  oyster  can  and  paint  one  side  with 
the  lampblack.  Fill  this  third  can  with  boiling  water  and  place 
it  on  the  wooden  strips,  midway  between  the  two  tin  bulbs,  the 
two  blackened  surfaces  facing  each  other.  The  heat  radiated  and 
absorbed  by  the  two  blackened  surfaces  will  exceed  the  heat  radi- 
ated and  absorbed  by  the  two  equal  unpainted  surfaces  that  face 
each  other.  The  movement  of  the  colored  alcohol  in  the  tube  will 
show  this  to  be  true. 

625.  Sympathetic  Vibrations. — The  relation 
between  radiation  and  absorption  of  heat  is  closely  analo- 
gous to  the  relation  between  the  radiation  and  absorption 
of  sound.  If  a  set  of  sound  waves  fall  upon  a  string 
capable  of  producing  similar  waves,  the  string  is  set  in 
motion  and  the  sound  waves  weakened  (§  509).  When 
ether  waves  of  a  given  kind  fall  upon  a  body  whose  mole- 
cules are  able  to  vibrate  at  the  same  rate,  and  thus  to 
reproduce  similar  waves,  the  kinetic  energy  is  transferred 
from  the  ether  to  the  molecules,  the  molecules  are  heated, 
the  radiant  energy  absorbed.  This  ability  to  absorb  wave 
motion  of  any  particular  kind,  implies  the  ability  to  repro- 
duce the  same  kind  of  waves.  It  therefore  is  easily  seen 


MODES  OF  DIFFUSING  HEAT.  461 

that  a  body  that  can  absorb  any  particular  kind 
of  heat  rays  can  radiate  the  same  kind. 


.  —  It  will  be  seen  further  on,  that  obscure  heat  rays  diffei 
from  light  only  in  the  matter  of  icave  length.  Most  of  the  phenomena 
of  one  may  be  shown  to  pertain  to  the  other.  Absorption,  radiation, 
reflection,  transmission  and  refraction  of  rays  follow  the  same  laws, 
whether  the  agent  be  called  heat  or  light.  Other  phenomena,  such 
as  interference  and  polarization,  more  satisfactorily  studied  with 
luminous  rays,  have  been  produced  with  obscure  rays.  It  should 
be  borne  in  mind  that  the  most  delicate  instruments  yet  made  are 
far  less  sensitive  to  obscure  heat  than  is  the  eye  to  light.  A  candle 
flame  may  be  seen  a  mile  away  ;  any  one  might  well  be  pleased  with 
an  instrument  that  would  detect  its  heat  at  the  distance  of  a  rod. 

QUESTIONS. 

1.  Good  conductors  feel  warmer  or  cooler  to  the  touch  than  poor 
conductors  of  the  same  temperature.     Why  ? 

2.  Why  is  it  so  oppressively  warm  when  the  sun  shines  after  a 
summer  shower  ? 

3.  Why  is  there  greater  probability  of  frost  on  a  clear  than  on 
a  cloudy  night  ? 

4.  Can  a  good  absorbent  be  a  good  reflector  of  heat  ?    Is  a  good 
absorbent  a  good  radiator,  or  otherwise  ? 

5.  Explain  why  the  glass  covering  of  a  hot-bed  or  conservatory 
renders  the  confined  air  warmer  than  the  atmosphere  outside. 

6.  From  your  own  experience,  decide  which  is  the  better  con- 
ductor of  heat,  linen  or  woolen  goods,  oil-cloth  or  carpet. 

7.  Why  are  the  double  walls  of  ice-houses  filled  with  sawdust-? 
Why  do  fire-proof  safes  have  double  walls  inclosing  plaster-of- 
Paris  or  alum  ? 

8.  Why  do  furnace  men,  firemen   and  harvesters  wear  woolen 
clothing  ?    Explain  the  use  of  double  windows. 

9.  How  may  heat  be  diffused  ?    How  is  the  surface  of  the  earth 
and  how  is  the  atmosphere  heated  ?     Can  you  boil  water  in  a  vessel 
with  heat  applied  from  above  ?    Why? 

Recapitulation.  —  In  this  section  we  have  considered 
Conduction;  the  conductivity  of  Fluids;  Con- 
vection; the  Luminiferous  Ether,  its  Den* 


4  02  THERMODYNAMICS. 

sity  and  Elasticity ;  Radiant  Heat,  and 
diation ;  Diathermancy;  Selective  Absorp- 
tion ;  Reflection  from  plane  and  concave  surfaces ; 
Refraction  ;  the  Change  from  radiant  into  sensible 
heat;  the  determination  of  Absorbing,  Reflecting 
and  Radiating  Powers,  and  their  Mutual  Re- 
lations ;  Sympathetic  Vibrations. 


V, 


THERMODYNAM  ICS. 

626.  Definition  of  Thermodynamics.—  Ther- 
modynamics is  the  branch  of  science  that  considers 
the  connection  between  heat  and  inechanical  work. 
It  has  especial  reference  to  the  numerical  relation  between 
the  quantity  of  heat  used  and  the  quantity  of  work  done. 

627.  Correlation  of  Heat  and  Mechanical  Energy. 

—  We  know  that  heat  is  not  a  form  of  matter  because  it  can  be 
created  in  any  desired  quantity.  We  must  continually  remember 
that  it  is  a  form  of  energy.  When,  heat  is  produced  some  other 
kind  of  energy  must  be  destroyed.  Conversely,  when  heat  is  de- 
stroyed, some  other  form  of  energy  is  created.  Considered  as  heat 
merely,  this  agent  may  be  annihilated  ;  considered  as  energy,  it 
may  only  be  transformed.  The  most  important  transformations  of 
energy  are  those  between  heat  and  mechanical  energy.  The  process 
of  working  these  transformations  will  be  considered  directly.  It  is 
to  be  noticed,  however,  that  while  we  may  be  able  to  effect  a  total 
conversion  of  mechanical  energy  into  heat,  we  are  not  able  to  bring 
about  a  total  conversion  of  heat  into  mechanical  energy. 

628.  Heat  from  Percussion.  —  A  small  iron  rod 
placed  upon  an  anvil  may  he  heated  to  redness  hy  repeated 
blows  of  a  hammer.  The  energy  of  the  moving  mass  is 


THERMOD  YNAMICS. 


463 


broken  up,  so  to  speak,  and  distributed  among  the  mole- 
cules, producing  that  form  of  molecular  motion  that  we  call 
heat.  The  same  transformation  was 
illustrated  in  the  kindling  of  a  fire  by 
the  "flint  and  steel "  of  a  century  ago, 
It  may  be  experimentally  illustrated 
by  the  "air-syringe." 

(a.)  The  air-syringe  consists  of  a  cylinder 
of  metal  or  glass  and  an  accurately  fitting 
piston.  By  suddenly  driving  in  the  piston, 
the  air  is  compressed  and  heat  developed. 
A  bit  of  gun  cotton  previously  placed  in 
the  cylinder  may  thus  be  ignited.  If  the 
cylinder  be  made  of  glass,  and  a  bit  of  ordi- 
nary cotton  dipped  in  carbon  disulphide  be 
used,  repeated  flashes  of  light  may  be  pro- 
duced by  successive  combustions  of  ether 
vapor.  The  fumes  of  one  combustion 
must  be  blown  away  before  the  next  com- 
bustion is  attempted. 

629.  Heat  from  Friction.— 

Common  matches  are  ignited  and  cold 
hands  warmed  by  the  heat  developed 
by  friction.  It  is  said  that  some  savages  kindle  fires 
by  skilfully  rubbing  together  well-chosen  pieces  of  wood. 
In  the  case  of  the  axles  of  railway  cars  and  ordinary  car- 
riages, this  conversion  of  mechanical  energy  into  heat  is 
not  so  difficult  as  its  prevention.  Lubricants  are  used  to 
diminish  the  friction  and  prevent  the  waste  of  energy  due 
to  the  undesirable  transformation.  A  railway  train  is 
really  stopped  by  the  conversion  of  its  motion  into  heat. 
When  this  has  to  be  done  quickly,  the  change  is  hastened 
by  increasing  the  friction  by  means  of  the  brakes.  Ex- 
amples of  this  change  are  matters  of  every  day  experience. 


FIG.  313. 


464 


THE  R  MOD  TNAMICS. 


(a.)  Attach  a  brass  tube  10  cm.  long,  about  2  cm.  in  diameter  and 
closed  at  the  bottom,  to  a  whirling  table.  Partly  fill  the  tube  with 
alcohol  and  cork  the  open  end.  Press  the  tube  between  two  pieces 
of  board  hinged  together  as  shown  in  the  figure.  The  boards  should 


FIG.  314. 

have  two  grooves  for  the  reception  of  the  tube ;  the  inner  faces  of 
the  boards  may  be  covered  with  leather.  When  the  machine  is  set 
in  motion,  the  friction  warms  and  soon  boils  the  alcohol.  The  vapor 
drives  out  the  cork  with  explosive  violence. 

630.  First  Law  of  Thermodynamics.— -When 
heat   is    transformed    into   mechanical    energy   or 
mechanical  energy  into  heat,  the  quantity  of  heat 
equals  the   quantity   of  mechanical   energy.     This 
principle  is  the  corner-stone  of  thermodynamics.    It  is 
a  particular  case  under  the  more  general  law  of  the  Con- 
servation of  Energy. 

631.  Joule's  Equivalent.— It  is  a  matter  of  great 
importance  to  determine  the  numerical  relation  between 
heat  and  mechanical  energy ;  to  find  the  equivalent  of  a 
heat  unit  in  units  of  work.     This  equivalent  was  first 
Ascertained  by  Dr.  Joule,  of  Manchester,  England.    Hi§ 


THERMODYNAMICS.  465 

experiments  were  equal  in  number  and  variety  to  the  im- 
portance of  the  subject.  He  showed  that  the  mechanical 
value  of  the  heat  required  to  warm  a  given  weight  of 

water  — 

(    424  meters  against  gravity. 
I'd.,  would  lift  the  water  ..........  1^90  feet 

1°  F.,  would  lift  the  water  ............    772    " 

and  represents  41,552,000,000  ergs  per  calorie. 

Any  weight  unit  may  be  used  without  changing  the 
above  values  which  should  be  remembered. 

Keferring  to  centigrade  degrees,  we  say  that  the 
mechanical  value  of  a  calorie  is  424  kilogrammeters  or 
that  of  the  third  unit  (§  579  a)  is  1,390  foot-pounds. 

Eef  erring  to  the  fourth  heat  unit  mentioned  in  §  579  («), 
we  say  that  its  mechanical  value  is  772  foot-pounds. 

632.  The  Use  of  Joule's  Equivalent.—  The 

use  of  the  mechanical  equivalent  of  heat  may  be  well  shown 
by  the  solution  of  a  problem. 

(a.)  If  a  cannon-ball  weighing  192.96  pounds  and  moving  with  a 
velocity  of  2000  feet  per  second,  be  suddenly  stopped  and  all  of  its 
kinetic  energy  converted  into  heat,  to  what  temperature  would  it 
warm  100  pounds  of  ice-cold  water  ? 

wtf       192.96  x  4000000 
Kinetic  energy  =  --—  =  —  —  =  12000000  foot-pounds. 


12000000  •*-  772  =  15544  +  heat  units. 

15544  -f-  100  =  155.44  heat  units  for  each  pound  of  water.  This 
would  raise  the  temperature  155.44°  R,  leaving  it  at  187.44°  F.  Ans. 

(6.)  Knowing  the  weight  of  the  earth  and  its  orbital  velocity,  we 
may  easily  compute  the  amount  of  heat  that  would  be  developed  by 
the  impact  of  the  earth  against  a  target  strong  enough  to  stop  its 
motion.  The  heat  thus  generated  from  the  kinetic  energy  of  the 
earth  would  be  sufficient  to  fuse  if  not  vaporize  it,  equalling 
that  derivable  from  the  combustion  of  fourteen  globes  of  coal 
each  equal  to  the  earth  in  size.  After  the  stoppage  of  its  orbital 
motion  it  would  surely  be  drawn  to  the  sun  with  continually 
increasing  velocity.  The  heat  instantaneously  developed  from 


466 


THERMO D  YNAMICS. 


this  impact  of  the  planetary  projectile  would  equal  that  derivable 
from  the  combustion  of  5600  globes  of  coal  each  equal  to  the  earth 
in  size.  This  is  the  measure  of  the  potential  energy  of  the  earth 
considered  as  a  mass  separated  from  the  &un. 

633.  Chemical  Affinity.— We  have  already  seen 
that  there  are  forces  in  nature  compared  with  which  the 
force  of  gravity  is  insignificant.     (Read  carefully  the  first 
paragraph  in  this  chapter.)     When  coal  is  burned,  the 
carbon  and  oxygen  particles  rush  together  with  tremendous 
violence,  energy  of  position  being  converted  into  energy  of 
motion.     The  molecular  motions  produced  by  this  clashing 
of  particles  constitute  heat  and  have  a  mechanical  value. 

634.  Heat  Equivalent  of  Chemical  Union.— 

If  a  pound  of  carbon  be  burned,  the  heat  of  the  combus- 
tion would  raise  about  8,000  pounds  of  water  1°  C.  In 
like  manner,  the  combustion  of  a  gram  of  hydrogen  would 
yield  about  34,000  lesser  calories. 

(a.)  The  following  table  shows  the  heating  powers  of  several 
substances  when  burned  in  oxygen  : 


Hydrogen 34,462 

Marsh  gas  (CH4) 13,063 

Petroleum 12,300 

Carbon 8,080 


Alcohol  (C3H60) 6,850 

Phosphorus ....  5,747 

Carbon  protoxide  (CO) 2,403 

Sulphur 2,220 


(6.)  The  calorific  powers  mentioned  above  may  be  adapted  to  Fah- 
renheit degrees  by  multiplying  them  respectively  by  f .  As  they 
stand,  the  numbers  represent  the  number  of  times  its  own  weight 
of  water  that  could  be  warmed  1°  C.  by  burning  the  substance  in 
oxygen. 

635.  The  Steam -Engine.—  The  steam-engine  is  a 
machine  for  utilizing  the  tension  of  steam.  Its  essential 
parts  are  a  boiler  for  the  generation  of  steam,  and  a  cylinder 
for  the  application  of  the  tension  to  a  piston. 


THE  STEAM-ENGINE.  467 

(a.)  As  in  the  case  of  water-power  the  production  of  mechanical 
kinetic  energy  involves  the  fall  of  water  from  a  higher  to  a  lower 
level,  so  in  the  case  of  steam-power  the  production  of  visible 
energy  involves  the  fall  of  heat  from  a  higher  to  a  lower  temper- 
ature. 

636.  Single-Acting   Engine.— In  a  single-acting  steam 
engine,  the  piston  is  pushed  one  way  by  the  tension  of  the  steam, 
The  steam  is  then  condensed  and  the  piston  driven  back  by  atmos 
pli eric  pressure.     Such  engines  have  gone  out  of  use  and  have  only 
an  historical  interest. 

637.  Double  -  Acting   Engine.  — In  a  double- 
acting  steam-engine,  the  steam  is  admitted  to  the  cylinder 
alternately  above  and  below  the'  piston.     This  alternate 
admission  of  the  steam  is  accomplished  by  means  of  a 
sliding-valve.    The  sliding-valve  is  placed  in  a  steam-chest, 
S9  which  is  fastened  to  the  side  of  the  cylinder  C. 


FIG.  315. 

(a. )  In  the  figure,  the  steam-chest  is  represented  as  being  placed 
tit  a  distance  from  the  cylinder;  this  is  merely  for  the  purpose 
of  making  plain  the  communicating  passages  to  and  from  the 
chest.  Steam  from  the  boiler  enters  at  M,  passes  through  A  to  the 


468  THE  STEAM-ENGINE. 


FIG.  316. 

cylinder,  where  it  pushes  down  the  piston  as  indicated  by  the 
arrows.  The  steam  below  the  piston  escapes  by  B  and  N.  As  the 
piston  nears  the  opening  of  B  in  the  cylinder,  the  sliding- valve  is 
raised,  by  means  of  the  rod  R,  to  the  position  indicated  in  Fig. 
267.  Steam  now  enters  the  cylinder  by  B  and  pushes  up  the  piston. 
The  steam  above  the  piston  escapes  by  A  and  N.  As  the  piston 
nears  the  opening  of  A  in  the  cylinder,  the  sliding- valve  is  pushed 
down  by  R  and  the  process  is  thus  repeated.  The  piston-rod  and 
the  sliding-valve  rod  work  through  steam-tight  packing -boxes. 
(Appendix  S.) 

638.  The  Eccentric. — By  means  of  a  crank  or 
similar  device,  illustrated  in  common  foot-power  machinery 
like  the  turning-lathe,  scroll-saw,  or  sewing-machine,  the 
alternating  rectilinear  motion  of  the  piston-rod  is  changed 
into  a  continuous  rotary  motion.  A  circular  shaft  is  thus 
given  a  revolution  for  every  to-and-fro  movement  of  the 
piston.  This  shaft  generally  carries  an  eccentric  for  work- 
ing the  sliding-valve  rod  R.  The  eccentric  (Fig.  317)  con- 
sists of  a  circular  piece  of  metal,  0,  rigidly  attached  to  the 
shaft  of  the  engine  8,  in  such  a  position  that  the  centre  of 
the  piece  does  not  coincide  with  the  centre  of  the  shaft, 


THE  STEAM-ENGINE. 


469 


The  eccentric  turns  within  a  collar,  which  is  fastened  to 
the  frame  T.  Every  turn  of  the  shaft  moves  the  eccentric 
with  its  collar  and  the  frame  T,  backward  and  forward  into 
the  two  positions  indicated  by  the  full  and  dotted  lines  of 


FIG.  317. 

Fig.  317.  The  point  a  may  be  fastened  directly  to  the 
slidirig-valve  rod  or  through  the  agency  of  the  bent  lever, 
abc,  as  the  circumstances  of  the  case  render  more  desirable. 

639.    The   Governor   and   Fly- Wheel.— The 

admission  of  steam  through  M  (Fig.  316)  is  regulated  by  a 
throttle  valve  worked  by  a  governor  (Fig.  318).  A  vertical 
shaft  is  given  a  rotary  motion  by  the  machinery.  To  the 
top  of  this  rod  are  hinged  two  arms  carrying  heavy  balls,  fib. 
From  these  arms,  supports  extend  to  a 
collar,  c,  surrounding  the  vertical  rod. 
This  collar  is  connected  with  a  valve  con- 
trolling the  admission  of  steam  to  the 
valve-chest  in  such  a  way  that  when  the 
collar  rises  the  valve  closes.  As  the 
machinery  increases  its  speed,  the  balls 
revolve  more  rapidly  about  the  vertical 
axis  and  tend  to  fly  further  apart  (§  74). 
In  doing  so,  they  raise  the  collar  and  partly  close  the  valve, 
diminishing  the  supply  of  steam.  The  machinery  is  thus 
made  to  slacken  its  speed,  the  balls  fall,  and  the  valve  opens. 
The  rapidity  of  motion  can  therefore  be  confined  within 


FIG.  318. 


470 


THE  STEAM-ENGTNE. 


FIG.  319. 


the  limits  due  to  closing  the  throttle-valve  and  throwing 
it  wide  open.  Further  than  this,  smoothness  of  motion  is 
secured  by  attaching  a  heavy  fly-wheel  to  the  shaft  of  the 
engine.  A  little  reflection  will  show  that  the  fly-wheel 
also  acts  as  an  accumulator  of  energy. 

O4O.  The  Safety- Valve.— The  safety-valve  is  a 
necessary  part  of  every  steam-boiler.  It  consists  of  a 
valve,  V,  held  down  over  an  opening  in  the  top  of  the 
boiler  by  means  of  a  spring  or  a 
loaded  lever  of  the  second  class. 
The  force  with  which  the  valve 
is  held  down  is  to  be  less  than 
the  strength  of  the  boiler,  i.  e., 
the  force  must  be  such  that  the 
valve  will  open  before  the  tension 

of  the  steam  becomes  dangerous.  On  steamboats,  the 
weight,  W,  is  generally  locked  in  position  by  a  Government 
officer. 

641.    Non-Condensing    Engines.— When   the 

steam  is  forced  out  at  N  (Fig.  316),  it  has  to  overcome  an 
atmospheric  pressure  of  15  pounds  to  the  square  inch. 
This  must  be  deducted  from  the  total  tension  of  the  steam 
to  find  the  available  power  of  the  engine.  Such  an  engine 
is  known  as  a  non-condensing  engine.  It  may  be  recog- 
nized by  the  escape  of  steam  in  puffs.  It  is  generally  a 
high-pressure  engine.  The  railway  locomotive  is  a  high- 
pressure,  non-condensing  engine. 

(a.)  Only  a  small  part  of  the  heat  developed  by  the  combustion  of 
the  fuel  can  be  converted  into  mechanical  energy  by  the  engine. 
Most  of  it  passes  off  in  the  exhaust  steam,  still  existing  as  lieat 
which  is  wasted,  so  far  as  useful  effect  is  concerned.  The  ratio 
between  the  heat  delivered  to  the  engine  and  the  heat  converted  for 


THE  STEAM-ENGINE.  471 

doing  the  work  is  called  the  efficiency  of  the  engine.  "It  is  not 
possible,  even  with  a  perfect  engine,  to  convert  into  work  more  than 
15  per  cent,  of  the  heat  used." 

642.  Condensing  Engines. — The  steam  may  be 
conducted  from  the  exhaust  pipe,  N  (Fig.  316),  to  a  chamber 
called  a  condenser.     Steam  from  the  cylinder  and  a  jet  of 
cold  water  being  admitted  at  the  same  time,  a  vacuum  is 
formed  and  the  loss  of  energy  due  to  atmospheric  pressure 
is  avoided.     Such  an  engine  is  known  as  a  condensing,  or 
low-pressure  engine. 

(a.)  Low-pressure  engines  are  always  condensing  engines.  A  low- 
pressure  engine  will  do  more  work  with  a  given  amount  of  fuel 
than  a  high-pressure,  non-condensing  engine  will,  is  less  liable  to 
explosion,  and  causes  less  wear  and  tear  to  the  machinery.  But  it 
must  be  larger,  more  complicated,  more  costly  and  less  portable. 

643.  Heat  and  Work  of  Steam-Engines.— - 

More  heat  is  carried  to  the  cylinder  of  a  steam-engine  than 
is  carried  from  it.  The  piston  does  work  at  every  stroke 
and  this  work  comes  from  the  heat  that  disappears.  Every 
stroke  of  the  piston  annihilates  heat.  Careful  experiments 
show  that  the  heat  destroyed  and  the  work  performed  are 
in  strict  agreement  with  Joule's  equivalent.  With  a  given 
supply  of  fuel,  the  engine  will  give  out  less  heat  when  it 
is  made  to  work  hard  than  when  it  runs  without  doing 

much  work. 

EXERCISES. 

1.  The  mechanical  equivalent  of  heat  is  1,390  foot-pounds.    What 
is  it  in  kilogrammeters  ? 

2.  Find  the  weight  of  water  that  may  be  warmed  15°  C.  by  burn- 
ing 1  ounce  of  sulphur  in  oxygen.  Ans.  148  oz. 

3.  What  weight  of  water  would  be  heated  from  0°  C.  to  1°  C.  by 
the  combustion  of  one  gram  of  phosphorus  ?  Ans.  5,747  g. 

4.  One  gram  of  hydrogen  is  burned  in  oxygen.    To  what  tempera- 
ture would  a  kilogram  of  water  at  0°  C.  be  raised  by  the  combustion  V 

5.  From  what  height  must  a  block  of  ice  at  0°  C.  fall  that  the  heat 
generated  by  its  collision  with  the  earth  shall  be  just  able  to  melt  it  7 


472  THERMODYNAMICS. 

6.  From  what  height  must  it  fall  that  the  heat  generated  may  be 
sufficient  to  vaporize  it  ?  Am.  996,630  ft.  in  vacuo. 

7.  To  what  height  could  a  ton  weight  be  raised  by  utilizing  all  the 
heat  produced  by  burning  5  Ib.  of  pure  carbon  ?       Am.  28,078  ft. 

8.  Find  the  height  to  which  it  could  be  raised  if  the  coal  had  the 
following  percentage  composition : 

C  =  88.42 ;    H  =  5.61 ;  0  =  5.97. 

9.  To  what  temperature  would  a  cannon-ball  weighing  150  Ib. 
and  moving  1,920  feet  per  sec.,  warm  2,000  Ib.  of  water  at  32°  F.,  if 
its  motion  were  suddenly  converted  into  heat  ?  Am.  37£°  F. 

10.  (a.)  How  many  pounds  of  water  can  be  evaporated  by  80  Ib. 
of  pure  carbon  ?    (6.)  If  applied  to  iron,  how  many  pounds  could  be 
heated  from  0°  F.  to  2,000°  F,  ?     Ans.  (a.)  Not  more  than  1,203.72  Ib. 

11.  With  what  velocity  must  a  10-ton  locomotive  move  to  give 
a  mechanical  energy  equivalent  to  the  heat  necessary   to  convert 
48  pounds  of  ice  at  0°  C.  to  steam  at  100°  C.?  Ans.  392  ft. 

12.  An  8-lb.  ball  is  shot  vertically  upward  in  a  vacuum  with  a 
velocity  of  2,000  feet.     How  many  pounds  of  water  may  be  raised 
from  the  freezing  to  the  boiling  point  by  the  heat  generated  when 
it  strikes  the  earth  on  its  descent  ?  Ans.  3.57  Ib. 

13.  (a.)  From  what  height  must  water  fall  in  order  to  raise  its 
own  temperature  1°  C.  by  the  destruction  of  the  velocity  acquired, 
supposing  no  other  body  to  receive  any  of  the  heat  thus  generated? 
(Answer  to  be  given  in  meters.)     (&.)  How  far  must  mercury  fall  to 
produce  the  same  effect?     (Specific  heat  of  mercury  =  .0333.) 

14.  With  a  velocity  of  how  many  cm.  per  second  must  a  leaden 
bullet  strike  a  target  that  its  temperature  may  be  raised  100°  C.  by 
the  collision,  supposing  all  the  energy  of  the  motion  to  be  spent  in 
heating  the  bullet  ?    (Specific  heat  of  lead=.0314;  ^=980  cm.    %  127.) 

15.  A  steam-engine  raises  a  ton  weight  386  ft.    How  many  calories 
are  thus  expended  ? 

16.  A  64-pound  cannon-ball  strikes  a  target  with   a  velocity  of 
1,400  feet  per  second.     Supposing  all  the  heat  generated  to  be  given 
to  60  pounds  of  water,  how  many  centigrade  degrees  would  the 
temperature  of  the  water  be  raised  ?  Ans.  23.3. 

17.  A  cannon  ball  weighing  7  pounds  strikes  an  iron  target  with  a 
velocity  of  1,000  feet  per  second.     Suppose  the  whole  of  the  motion 
to  be  converted  into  heat  and  the  heat  uniformly  distributed  through 
70  pounds  of  the  target,  determine  the  change  of  temperature  thus 
produced.     (Specific  heat  of  iron  =  .1138.)  Ans.  17.7°  F. 

18.  The  specific  heat  of  tin  is  .056  and  its  latent  heat  of  fusion  is 
25.6  Fahrenheit  degrees.     Find  the  mechanical  equivalent  of  the 
amount  of  heat  needed  to  heat  6  pounds  of  tin  from  374°  F.  to  its  melt- 
ing point,  442°  F.,  and  to  melt  it.       Ans.  136,217.856  foot-pounds. 


REVIEW.  473 

Recapitulation. — In  this  section  we  have  considered 
the  definition  of  Thermodynamics ;  the  Corre- 
lation of  Heat  and  Mechanical  Energy ; 
heat  from  Percussion ;  from  Friction ;  First 
Law  of  thermodynamics;  Joule's  Equivalent 
and  its  Use ;  Chemical  Affinity  and  the  Heat- 
ing Powers  of  various  substances ;  the  Single  and 
Double-acting  Steam-engines ;  the  Eccen- 
tric, Governor  and  Safety-valve  ;  Condens- 
ing and  Non-condensing  Engines  ;  the  relation 
between  Heat  and  Work  in  the  steam-engine. 

REVIEW  QUESTIONS  AND  EXEKCISES. 

1.  Lead  melts  at  326°  C.    In  melting  it  absorbs  about  as  much 
heat  as  would  warm  5.37  times  its  weight  of  water  1°C.     What 
numbers  will  replade  the  326  and  5.37  when  the  Fahrenheit  scale  is 
used? 

2.  What  is  the  difference  between  the  temperatures— 40°  C.  and 
-40°  F.  ? 

3.  A  quantity  of  gas  at  100°  C.  and  under  a  pressure  of  750  mm.  of 
mercury  measures  4500  cu.  cm.    What  will  be  its  volume  at  200°  C. 
and  under  a  pressure  of  76  cm.  of  mercury  ?     Ans.  5,631  cu.  cm. 

4.  Over  how  high  a  ridge  can  you  carry  water  in  a  siphon,  where 
the  minimum  range  of  the  barometer  is  27  inches  ?    Explain. 

5.  («.)  What  is  Specific  Gravity  ?  (6.)  How  do  you  find  that  of  solids 
heavier  than  water  ?    (c.)  What  principle  is  involved  in  your  method  ? 

6.  (a.)  Of  what  physical  force  is  lightning  a  manifestation  ?    (6.) 
Give  some  plain  directions  for  the  construction  of  lightning-rods, 
with  reasons  for  your  directions. 

7.  Give  the  fundamental  principle  of  mechanics,  and  illustrate  its 
application  by  one  of  the  mechanical  powers. 

8.  (a.)  What  are  the  essential  properties  of  matter?  (&.)  What  is  a 
pendulum  ;  (c.)  to  what  use  is  it  principally  applied,  and  (d.)  what 
are  the  laws  by  which  it  is  governed  ? 

9.  (a.)  In  what  ways  may  two  musical  tones  differ?    (&.)  What  ia 
the  physical  cause  of  the  diffe^nce  in  each  case  ? 

10.  (a.)  Convert  -3°  F.  and  77°  F.  into  G-  readings ;    (6.)  18°  C 
and  20°  C.  to  F.  readings. 


474 


11.  (a.)  To  what  temperature  should  a  liter  of  oxygen  at  0°  C.  be 
raised  in  order  to  double  its  volume,  the  pressure  remaining  con- 
stant?   (b.)  Give  reasons  for  your  answer.    Ans.  273°  C. 

12.  (a.)  What  is  meant  by  the  boiling  point  of  a  liquid  ?    (&.)  State 
some  circumstances  that  cause  it  to  vary. 

13.  A  kilogram  each  of  water,  iron  and  antimony,  at  0°  C.  are 
heated  ten  minutes  by  the  same  source  of  heat,  and  are  then  found 
to  be  1°  C.,  9°  C.  and  20°  C.  respectively.    Kequired  the  specific  heat 
of  each. 

14.  (a.)  Define  latent  heat.     (&.)  Describe  a  method  of  determining 
the  latent  heat  of  water,    (c.)  Describe  the  cooling  and  freezing  of 
a  lake. 

15.  (a.)  If  2  kilograms  of  water  should  be  suddenly  stopped  after 
falling  212  metres,   how  much  heat  would  be  generated?     (6.) 
Describe  the  essential  parts  of  a  steam-engine. 

16.  (a.}  How  many  cubic  feet  of  water  will  be  displaced  by  a  boat 
weighing  two  tons  ?     (&.)   How  many  of  salt  water  of  sp.  gr.  1.09  ? 
(c.)  How  does  a  noise  differ  from  a  musical  sound  ? 

17.  The  sp.  gr.  of  alcohol  is  .8  ;  that  of  mercury  13.6.    When  a 
mercury  barometer  indicates  a  pressure  of  30  inches,  what  will  be 
the  height  of  an  alcohol  barometer  column  ?     Ans.  510  in. 

18.  (a.)  Describe  the  ordinary  force-pump  ;  (&.)  explain  the  use  of 
its  essential  parts. 

19.  («.)  Give  the  formulas  for  changing  thermometric  readings 
from  F.  to  C.,  and  vice  versa.     (&.)  Explain  the  graduation  of  two 
kinds  of  thermometers,    (c.)  Define  increment  of  velocity. 

20.  (a.)  What  is  distillation,  and  upon  what  fact  does  the  process 
depend?    (&.)  What  is  latent  heat?    (c.)  Illustrate  the  conversion 
of  sensible  into  latent  heat,     (d.)  On  what  does  the  pitch  of  sound 
depend  ? 

21.  (a.)  Define  boiling  and  boiling-point.    (6.)  What  is  the  rate  of 
expansion  for  gases  ?    (c.)  Will  water  boil  at  a  lower  temperature 
at  the  sea  level  or  on  the  top  of  a  mountain  ?    Why  ?    (d.}  What 
constitutes  the  timbre  of  a  sound  ?    (e.)  Give  the  formulas  for  the 
wheel  and  axle. 

22.  (a.)  If  the  pressure  remain  the  same,  how  much  will  546  cu.  cm. 
of  hydrogen  expand  when  heated  from  0°  C.  to  10°  C.  ?    (&.)  How 
much  work  may  be  performed  by  a  ball  weighing  64.32  lb.,  moving 
with  a  velocity  of  50  ft.  per   second?     (c.)  When  has  water  the 
greatest  density  ?          Ans.  (a.)  20  cu.  cm.    (&.)  2,500  foot  -pounds. 

23.  Show  that  to  raise  the  temperature  of  a  pound  of  iron  from 
0°  C.  to  100°  C.  requires  more  energy  than  to  raise  seven  tons  of  iron 
a  foot  high. 


IX. 


LIGHT. 


ECTJON  I. 


THE    NATURE,    VELOCITY   AND    INTENSITY 
OF    LIGHT. 

644.  What  is  Light?— Light  is  that  mode  of 
motion    which    is    capable    of  affecting    the  optic 
nerve.    The  only  physical  difference  between  light 
and  radiant  heat  is  one  of  wave  length. 

(a.)  We  have  seen  that  the  vibrations  of  air  particles  in  a  sound 
wave  are  to  and  fro  in  the  line  of  propagation.  In  the  case  of 
radiant  heat  and  light,  the  ether  particles  vibrate  to  and  fro  across 
the  line  of  propagation.  Vibrations  in  a  sound  wave  are  longitudi- 
nal ;  those  of  a  heat  or  light  wave  are  transversal. 

645.  Luminous  and  Non-Luminous  Bodies. 

— Bodies  that  emit  light  of  their  own  generating,  as  the 
sun  or  a  candle,  are  called  luminous.  Bodies  that  merely 
diffuse  the  light  that  they  receive  from  other  bodies  are 
said  to  be  non-luminous  or  illuminated.  Trees  and  plants 
are  non-luminous. 

(a.)  Visible  bodies  may  be  luminous  or  illuminated,  but  in  either 
case  they  send  light  in  every  direction  from  every  point  in  their 
surfaces.  In  Fig.  320  we  see  represented  a  few  of  the  infinite 
number  of  lines  of  light  starting  from  A,  B  and  C,  three  of  the 


476  THE  NATURE   OF  LIGHT. 

infinite  number  of  points  in  the  surface  of  a  visible  object.     If  the 

infinite  number  of  lines  were  drawn  from  each  of  the  infinite  number 
of  points,  there  would  be  no  vacant  spaces  in 
the  figure  ;   the  rays  really  intersect  at  every 
point  from  which  the  object  is  visible. 

646.  Transparent,    Translu- 
cent and  Opaque  Bodies. — Bodies 
are  transparent,  translucent  or  opaque 
according  to  the  degree  of  freedom  which 

they  afford  to  the  passage  of  the  luminiferous  waves. 
Transparent  bodies  allow  objects  to  be  seen  distinctly 
through  them,  e.  (/.,  air,  glass  and  water.  Translucent 
bodies  transmit  light,  but  do  not  allow  bodies  to  be  seen 
distinctly  through  them,  e.  g.,  ground  glass  and  oiled  paper. 
Opaque  bodies  cut  off  the  light  entirely  and  prevent 
objects  from  being  seen  through  them  at  all.  The  light 
is  either  reflected  or  absorbed.  So  much  of  the  radiant 
energy  as  is  neither  reflected  nor  transmitted  is  changed 
to  absorbed  heat. 

647.  Luminous  Rays. — A  single  line  of  light  is 
called  a  ray.    The  ray  of   light  is  perpendicular  to  the 
wave  of  ether.    The  ray  may,  without  considerable  error, 
be  deemed  the  path  of  the  wave. 

648.  Luminous  Beams  and  Pencils. — A  col- 
lection of  parallel  rays  constitutes  a  beam ;  a  cone  of  rays 
constitutes  a  pencil.     The  pencil  may  be  converging  or 
diverging.    If  a  beam  or  pencil  should  dwindle  in  thick- 
ness to  a  line,  it  would  become  a  ray. 

649.  Rectilinear  Motion  of  Light. — A  medium 
is  homogeneous  when  it  has  an  uniform  composition  and 
density.    In  #  homogeneous  medium,  light  travels 


TffE  NATURE  OF  LIGHT.  477 

in  straight  lines.     This  is  a  fact  of  incalculable  scien- 
tific and  otherwise  practical  importance. 

(a.)  The  familiar  experiment  of  "taking  sight"  depends  upon 
this  fact,  for  we  see  objects  by  the  light  which  they  send  to  the  eye. 
We  cannot  see  around  a  corner  or  through  a  crooked  tube.  A  beam 
of  light  that  enters  a  darkened  room  by  a  small  aperture,  marks  an 
illuminated  course  that  is  perfectly  straight. 

(&.)  This  fact  may  be  illustrated  by  providing  two  or  three  per- 
forated screens  and  arranging  them  as  shown  in  Fig.  321,  so  that 
the  holes  and  a  candle  flame  shall  be  in  the  same  straight  line. 


FIG.  321. 

When  the  eye  is  placed  in  this  line  behind  the  screens,  light  passes 
from  the  flame  to  the  eye ;  the  flame  is  visible.  A  slight  displace- 
ment upward,  downward  or  sidewise  of  the  eye,  the  flame  or  any 
screen,  cuts  off  the  light  and  renders  the  flame  invisible. 

(c.)  Prepare  a  piece  of  wood,  1|  x  2|  x  18  inches,  taking  care  that 
the  edges  are  square.  Saw  it  into  six  pieces,  each  three  inches  long. 
Prepare  three  pieces  of  wood,  3  x  4  x  ^  inches.  Place  three  postal 
cards  one  over  the  other  on  a  board,  and  pierce  them  with  a  fine 
awl  or  stout  needle,  |  inch  from  the  end  and  1*  inch  from  either 
side  of  the  card.  With  a  sharp  knife  pare  off  the  rough  edges  of 
the  holes,  and  pass  the  needle  through  each  hole  to  make  the  edges 
smooth  and  even.  Over  the  ^  x  3  inch  surface  of  one  of  the  blocks 
place  the  unperforated  end  of  one  of  the  postal  cards,  and  over  this 
place  one  of  the  3x4  inch  pieces,  so  that  their  lower  edges  shall  be 


478  THE  NATURE  OF  LIGHT. 

even.  Tack  them  in  this  position.  Make  thus  two  more  similar 
screens.  The  three  screens,  with  a  bit  of  candle  three  inches  long, 
placed  upon  one  of  the  remaining  blocks,  furnishes  the  material 
for  the  experiment  above.  Save  the  screens  and  three  blocks  for 
future  use.  (See  Fig.  329.) 

65O.  Inverted  Images.— If  light  from  a  highly- 
illuminated  body  be  admitted  to  a  darkened  room  through 
a  small  hole  in  the  shutter  and  there  received  upon  a  white 
screen,  it  will  form  an  inverted  image  of  the  object  upon 


FIG.  322. 

the  screen.  Every  visible  point  of  the  illuminated  object 
sends  a  ray  of  light  to  the  screen.  Each  ray  brings  the 
color  of  the  point  which  sends  it  and  prints  the  color  upon 
the  screen.  As  the  rays  are  straight  lines,  they  cross  at 
the  aperture;  hence,  the  inversion  of  the  image.  The 
image  will  be  distorted  unless  the  screen  be  perpendicular 
to  the  rays.  The  darkened  room  constitutes  a  camera 
obscura.  The  image  of  the  school  playground  at  recess  is 
very  interesting  and  easily  produced. 

(a.)  Place  a  lighted  candle  about  a  meter  from  a  white  screen  in 
a  darkened  room.  (The  wall  of  the  room  will  answer  for  the  screen.) 
Pierce  a  large  pin-hole  in  a  card  and  hold  it  between  the  flame  and 
the  screen.  An  inverted  image  of  the  flame  will  be  found  upon  the 
screen. 

(6.)  Bore  an  inch  hole  in  one  side  of  a  wooden  box ;  cover  thii 


THE  NATURE   OF  LIGHT.  479 

opening  with  tin-foil  and  prick  the  tin-foil  with  a  needle.  Place  a 
lighted  candle  within  the  box  ;  close  the  box  with  a  lid  or  a  shawJ 
and  hold  a  paper  screen  before  the  hole  in  the  tin-foil.  Move  the 
screen  backward  and  forward  and  notice  that  in  any  position  the 
size  of  the  object  is  to  the  size  of  the  image  as  the  distance  from 
the  aperture  to  the  object  is  to  the  distance  from  the  aperture  to  the 
image. 

(c.)  Cover  one  end  of  a  tube,  10  or  12  cm.^ong,  with  tin-foil ;  the 
other  end  with  oiled  paper.  Prick  a  pin-hole  in  the  tin-foil  and  turn 
it  toward  a  candle  flame.  The  inverted  image  may  be  seen  upon 
the  oiled  paper.  The  size  of  the  image  will  depend  upon  the  dis- 
tance of  the  flame  from  the  aperture.  The  apparatus  rudely  repre- 
sents the  eye,  the  pin-hole  corresponding  to  the  pupil  and  the  oiled 
paper  to  the  retina.  (Almost  any  housekeeper  will  give  you  an 
empty  tin  can.  Place  it  upon  a  hot  stove  just  long  enough  to  melt 
off  one  end,  thrust  a  stout  nail  through  the  centre  of  the  other 
end,  cover  the  nail-hole  with  tin-foil,  and  you  will  have  the  greater 
part  of  the  apparatus.) 

651.  Shadows.— Since  rays  of  light  are  straight, 
opaque  bodies  cast  shadows.  A  shadow  is  the  dark- 


FIG.  323. 

ened  space  behind  an  opaque  body  from  which  all 
rays  of  light  are  cut  off.  It  is  sometimes  called  the 
perfect  shadow  or  the  umbra.  If  the  source  of  light  be  a 
point,  the  shadow  will  be  well  defined ;  if  it  be  a  surface, 
the  shadow  will  be  surrounded  by  an  imperfect  shadow 
called  a  penumbra.  The  penumbra  is  the  darkened  space 


4&0  THE  NATURE   OF  LlGIfT. 

behind  an  opaque  body  from  which  some  of  the  rays  (the 
rays  from  a  part  of  the  luminous  surface)  are  cut  off. 

(a.)  Hold  a  lead  pencil  between  the  flame  of  an  ordinary  lamp 
and  a  sheet  of  paper  held  about  two  feet  (61  cm.)  from  the  lamp  ; 
(1.)  When  the  edge  of  the  flame  is  toward  the  pencil;  (2.)  When 
the  side  of  the  flame  is.  to  ward  the  pencil. 

652.  Visual  Angle. — The  angle  included  be- 
tween two  rays  of  light  coming  from  the  extrem- 
ities of  an  object  to  the  centre  of  the  eye  is  called 
the  visual  angle.  This  angle  measures  the  apparent 
length  of  the  line  that  subtends  it.  Any  cause  that 
increases  the  visual  angle  of  an  object  increases  its  appa- 
rent size.  Hence  the  effect  of  magnifying-glasses.  From 


FTG.  324. 

Fig.  324  we  see  that  equal  lines  may  subtend  different 
visual  angles,  or  that  different  lines  may  subtend  the  same 
angle. 

65.3.  Velocity  of  Light. — Light  traverses  the  ether 
with  a  velocity  of  about  186,000  miles  or  about  298  mil- 
lion meters  per  second.  This  was  first  determined  about 
200  years  ago  by  Roemer,  a  Danish  astronomer. 

(a.)  At  equal  intervals  of  42h.  28m.  36s.,  the  nearest  of  Jupiter's 
satellites  passes  within  his  shadow  and  is  thus  eclipsed.  This  phe- 
nomenon would  be  seen  from  the  earth  at  equal  intervals  if  light 
traveled  instantaneously  from  planet  to  planet.  Roemer  found 
that  when  the  earth  was  farthest  from  Jupiter  the  eclipse  was  seen 
16  min.  36  sec.  later  than  when  the  earth  was  nearest  Jupiter.  Bui 
Jupiter  and  the  earth  are  nearest  each  other  when  they  are  on  the* 


NATURE  OP  LIGHT.  481 

same  side  of  the  sun  and  in  a  straight  line  with  the  sun  (conjunc- 
tion), and  farthest  from  each  other  when  they  are  on  opposite 
aides  of  the  sun  and  in  a  straight  line  with  that  luminary  (opposi- 


FIG.  325. 

tion).  Hence,  Roemer  argued  that  it  requires  16  min.  36  sec.  for 
light  to  pass  over  the  diameter  of  the  earth's  orbit,  from  Eto  E'. 
This  distance  being  approximately  known,  the  velocity  of  light  is 
easily  computed. 

(6.)  The  velocity  of  light  has  been  measured  by  other  means, 
giving  results  that  agree  substantially  with  the  result  above  given. 
When  astronomers  accurately  determine  the  mean  distance  of  the 
earth  from  the  sun,  the  velocity  of  light  will  be  accurately  known. 

(c.)  It  would  require  more  than  17  years  for  a  cannon-ball  to  pass 
over  the  distance  between  the  sun  and  the  earth ;  light  makes  the 
journey  in  8  min.  18  sec.  For  the  swiftest  bird  to  pass  around  the 
earth  would  require  three  weeks  of  continual  flight ;  light  goes  as 
far  in  less  than  one  seventh  of  a  second.  For  terrestrial  distances, 
the  passage  of  light  is  practically  instantaneous  (§  487). 

654.  Effect  of  Distance  upon  Intensity.— 

The  intensity  of  light  received  by  an  illuminated 
body  varies  inversely  as  the  square  of  its  distance 
from  the  source  of  light. 

(a.}  Let  a  candle  at  8  be  the  source  of  light ;  A,  a  screen  one  foot 
square  and  a  yard  from  8 ;  B,  a  screen  two  feet  square  two  yards 
from  8;  0,  a  screen  three  feet  square  three  yards  from  S.  It 
will  easily  be  seen  that  A  will  cut  off  all  the  light  from  B  and  (7. 
If  now  A  be  removed,  the  quantity  of  light  which  it  received,  no 
more  and  no  less,  will  fall  upon  B.  If  now  B  be  removed,  the 
quantity  of  light  which  previously  illuminated  A  and  B  will  fall 
upon  C.  We  thus  see  the  same  number  of  rays  successively  illu 


8  'THE  ft  AZURE  OP  LICF&T. 

trfnating,  one,  four  and  nine  square  feet.    One  square  foot  at  B  will 

receive  one-fourth,  and  one 
square  foot  at  C  will  receive 
one-ninth  as  many  rays  as 
one  square  foot  at  A.  The 
light  being  diffused  over  a 
greater  surface  is  corres- 
pondingly diminished  in  in- 
tensity. 

(6.)  The  experiment  may 
be  tried  by  placing  the  large 
screen  at  A  and  tracing  the 
outline  of  the  shadow  with 
a  pencil,  then  placing  the 

FIG.  326.  screen  successively  at  B  and 

C,  tracing  the  shadow  each. 

time.     The  experiment  will  be  more  satisfactory  if  a  perforated 
screen  be  placed  at  8.    (See  First  Prin.  Nat.  Phil.,  §  428.) 

EXERCISES. 

1.  A  coin  is  held  5  feet  from  a  wall  and  parallel  to  it.     A  lumi 
nous  point,  15  inches  from  the  coin,  throws  a  shadow  of  it  upon  the 
wall.    How  does  the  size  of  the  shadow  compare  with  that  of  the  coin  ? 

2.  (a.)  What  is  the  velocity  of  light  ?    (&.)  How  was  it  determined  ? 

3.  (a.)  How  are  the  intensities  of  two  lights  compared  ?    (6.)  De- 
fine light,    (c.)  Give  your  idea  of  the  carrier  of  radiant  heat  and  light. 

4.  (a.)  Define  luminous,  transparent,  opaque,  beam  and  pencil. 
(6.)  How  could  you  show  that  light  ordinarily  moves  in  straight 
lines  ?    (c.)  Explain  the  formation  of  inverted  images  in  a  dark  room. 

5.  A  "  standard  "  candle  (burning  120  grains  of  sperm  per  hour)  is  2 
feet  from  a  wall,  a  lamp  is  6  feet  from  the  wall.   They  cast  shadows  of 
equal  intensity  on  the  wall.    What  is  the  "  candle  power  "  of  the  lamp  ? 

Recapitulation. — In  this  section  we  have  considered 
the  Nature  of  Light;  Luminous,  Illuminated, 
Transparent,  Translucent  and  Opaque  bodies ; 
Rays,  Beams  and  Pencils  of  light;  that  Light 
Moves  in  Straight  Lines;  Inverted  Images 
and  Shadows  ;  the  Visual  Angle  ;  the  Veloc- 
ity and  Intensity  of  light. 


THE  NATURE   OF  L1GHI.  48.') 


ECTION  II. 


REFLECTION    OF    LIGHT. 

Note.— The  heliostat,  or  porte-lumtire,  is  composed  of  one  oi 
more  mirrors,  by  means  of  which  a  beam  of  light  may  be  thrown 
in  any  desired  direction.  The  instrument  may  be  had  of  apparatus 
manufacturers  at  prices  ranging  from  $12  upward.  Directions  for 
making  one  may  be  found  in  Mayer  &  Barnard's  little  book  on 
"  Light,"  published  by  D.  Appleton  &  Co.  It  is  very  desirable  that 
the  instrument  be  secured  in  some  way. 

655.  Reflection. — If  a  sunbeam  enter  a  darkened 
room  by  a  hole  in  the  shutter,  as  at  A,  and  fall  upon  a 


FIG.  327. 

polished  plane  surface,  as  at  B,  it  will  be  continued  in  a 
different  direction,  as  toward  C.  AB  is  called  the  incident 
beam  and  EC  the  reflected  beam  (§  97).  The  incident 
and  the  reflected  beams  are  in  the  same  medium,  the  air. 
A  change  in  the  direction  of  light  mithout  a  change 
in  its  medium  is  called  reflection  of  light. 

656.  Laws  of  Reflection.— The  reflection  of  light 


484  REFLECTION  OF  LIGHT. 

from  polished  surfaces  is  m  accordance  with  the  following 
laws: 

(1.)  The  angle  of  incidence  is  equal  to  the  angle 
of  reflection. 

(2.)  The  incident  and  reflected  rays  are  both  in 
the  same  plane,  which  is  perpendicular  to  the 
reflecting  surface. 

(a.)  Fill  a  basin  to  the  brim  with  mercury  or  with  water  blackened 
with  a  little  ink.  In  this  liquid  suspend  by  a  thread  a  small 
weight  of  greater  specific  gravity  than  the  liquid  used  (§  253).  The 
plumb-line  will  be  perpendicular  to  the  liquid  mirror.  Let  the 
plumb-line  hang  from  the  middle  of  a  horizontal  meter  or  yard- 


FIG.  328. 


stick.  Place  the  tip  of  a  candle  flame  opposite  one  of  the  divisions 
of  the  stick,  and  place  the  eye  in  such  a  position  that  the  image  of 
the  top  of  the  flame  will  be  seen  in  the  direction  of  the  foot  of 
the  plumb-line.  Mark  the  point  where  the  line  of  vision  (i.  e.,  the 
reflected  rays)  crosses  the  meter- stick.  It  will  be  found  that  this 
point  and  the  tip  of  the  flame  are  equally  distant  from  the  middle 
of  the  stick.  From  this  it  follows  (Olney's  Geometry,  Art.  342) 
that  the  angles  of  incidence  and  of  reflection  are  equal. 

(&.)  Fig.  328  represents  a  vertical  semiaircle  graduated  to  degrees, 
with  a  background  of  black  velvet.  A  mirror  at  the  centre  is 
furnished  with  an  index  set  perpendicular  to  its  plane ;  both  mirror 
and  index  can  be  turned  in  any  direction  desired.  A  ray  of  light 
from  any  brilliant  source  is  allowed  to  enter  the  tube  at  the  base, 
in  the  direction  of  the  centre.  By  means  of  a  little  smoke  from 
brown  paper,  the  paths  of  the  incident  and  reflected  rays  are  easily 
shown  to  a  large  claws. 


REFLECTION  OF  LIGHT.  485 

(c.)  Place  two  of  the  screens  and  the  three  extra  blocks  men- 
tioned in  §  649  in  position,  as  shown  in  Fig.  329.  At  the  middle 
of  the  middle  block  place  a  bit  of  window  glass,  painted  on  the 
under  side  with  black  varnish.  On  the  blocks  that  carry  the  screens 
place  bits  of  glass,  n  and  o,  of  the  same  thickness  as  the  black  mir- 
ror on  the  middle  block.  Place  a  candle  flame  near  the  hole  in  one 
of  the  screens,  as  shown  in  the  figure.  Light  from  the  candle  will 
pass  through  A,  be  reflected  at  m,  and  pass  through  B.  Place  the 
eye  in  such  a  position  that  the  spot  of  light  in  the  mirror  may 
be  seen  through  B.  Mark  the  exact  spot  in  the  mirror  with  a 
needle  held  in  place  by  a  bit  of  wax.  Place  a  piece  of  stiff  writing 
paper  upright  upon  m  and  n,  mark  the  position  of  B  and  of  m, 
and  draw  on  the  paper  a  straight  line  joining  these  two  points. 
The  angle  between  this  line  and  tho  lower  edge  of  the  paper 
coincides  with  the  angle  Bmn.  Reverse  the  paper,  placing  it  upon 


FIG.  329. 

m  and  o.  It  will  be  found  that  the  same  angle  coincides  with 
Amo.  Amo  and  Bmn  being  thus  equal,  the  angle  of  incidence 
equals  the  angle  of  reflection. 

657.  Diffused  Light. — Light  falling  upon  an 
opaque  body  is  generally  divided  into  three  parts  :  the 
first  is  regularly  reflected  in  obedience  to  the  laws  above ; 
the  second  is  irregularly  reflected  or  diffused  ;  the  third  is 
absorbed.  The  irregular  reflection  is  due  to  the  fact  that 
the  bodies  are  not  perfectly  smooth,  but  present  little  pro- 
tuberances that  scatter  the  light  in  all  directions,  and  thus 
render  them  visible  from  any  position.  Light  regularly 
reflected  gives  an  image  of  the  body  from  which  it  came 
before  reflection ;  light  irregularly  reflected  gives  an  image 


486  REFLECTION  OF  LIGHT. 

of  the  body  that  diffuses  it.  A  perfect  mirror  would  be 
invisible.  Luminous  bodies  are  visible  on  account 
of  the  light  that  they  emit;  non-luminous  bodies 
are  visible  on  account  of  the  light  that  they  dif- 
fuse. 

(a.)  If  a  beam  of  light  fall  upon  a  sheet  of  drawing  paper,  it 
will  be  scattered  and  illuminate  a  room.  If  it  fall  upon  a  mirror, 
nearly  all  of  it  will  be  reflected  in  a  definite  direction,  and  intensely 
illuminate  a  part  of  the  room.  Place  side  by  side  upon  a  board 
a  piece  of  black  cloth  (not  glossy),  a  piece  of  drawing  paper  and  a 
piece  of  looking-glass.  In  a  darkened  room,  allow  a  beam  of  sun- 
light to  fall  upon  the  cloth  and  notice  the  absorption.  Let  it  fall 
upon  the  paper,  and  notice  the  diffusion  of  the  light  and  its  effects. 
Let  it  fall  upon  the  looking-glass,  and  notice  the  regular  reflection 
and  its  effects.  Move  the  board  so  that  the  cloth,  paper  and  glass 
ghall  pass  through  the  beam  in  quick  succession,  and  notice  the 
effects. 

(6.)  In  the  darkened  room  place  a  tumbler  of  water  upon  a  table  ; 
with  a  hand-mirror  reflect  a  sunbeam  down  into  the  water ;  the 
tumbler  will  be  visible.  Stir  a  teaspoonful  of  milk  into  the  water, 
and  again  reflect  the  sunbeam  into  the  liquid  ;  the  whole  room  will 
be  illuminated  by  the  diffused  light,  the  tumbler  of  milky  water 
acting  like  a  luminous  body. 

658.  Invisibility  of  Light.— Rays  of  light  that 
do  not  enter  the  eye  are  invisible.  A  sunbeam 
entering  a  darkened  room  is  visible  because  the  floating 
dust  reflects  some  of  the  rays  to  the  eye.  If  the  reflecting 
particles  of  dust  were  absent  the  beam  would  be  invisible. 

(a.)  Take  any  convenient  box,  about  60  cm.  (2ft.)  on  each  edge, 
provide  for  it  a  glass  front,  and,  at  each  end,  a  glass  window  about 
10cm.  (4  inches)  square.  Place  it  on  a  table  in  a  darkened  room, 
and,  with  the  heliostat,  send  a  solar  beam  through  the  windows. 
Standing  before  the  glass  front  of  the  box,  this  beam  may  be 
traced  from  the  heliostat  to  the  box,  through  the  box  and  beyond 
it.  Open  the  box,  smear  the  inner  surfaces  of  its  top,  back  and 
bottom  with  glycerine,  and  close  the  box  air-tight.  Allow  it  to 
remain  quiet  a  few  days ;  the  dust  in  the  box  will  be  caught  by 
the  glycerine  and  the  confined  air  thus  freed  from  particles  capablf? 


REFLECTION  OF  LIGHT.  487 

of  reflecting  light.  Then  send  another  solar  beam  from  the  helio- 
stat  through  the  two  windows  of  the  box.  Standing  as  before, 
the  beam  may  be  traced  to  the  box  and  beyond  it,  but  within  th« 
box  all  is  darkness. 

659.  Apparent  Direction  of  Bodies.— Ever} 

point  of  a  visible  object  sends  a  cone  of  rays  to  the  eye. 
The  pupil  of  the  eye  is  the  base  of  the  cone.  The  point 
always  appears  at  the  place  where  these  rays  seem 
to  intersect  (i.  e.9  at  the  real  or  apparent  apex  of  the  cone). 
If  the  rays  pass  in  straight  lines  from  the  point  to  the  eye, 
the  apparent  position  of  the  point  is  its  real  position.  If 
these  rays  bo,  bent  by  reflection,  or  in  any  other  manner, 
the  point  will  appear  to  be  in  the  direction  of 
the  rays  as  they  enter  the  eye.  No  matter  how 
devious  the  path  of  the  rays  in  coming  from  the  point  to 
the  eye,  this  important  rule  holds  good. 

660.  Plane  Mirrors;  Virtual  Images. — If  an 

object  be  placed  before  a  mirror,  an  image  of  it  appears 

behind  the  mirror.  In- 
asmuch as  the  rays  of 
the  cone  mentioned  in 
§  659  do  not  actually  con- 
verge back  of  the  mirror, 
there  can  be  no  real  image 
there.  As  there  really  is 
no  image  behind  the  mir- 
ror, we  call  it  a  virtual 
image.  All  virtual  images 
are  optical  illusions,  and 

are  to  be  clearly  distinguished  from  the  real  images  to  be 
studied  soon.  Each  point  of  this  image  will  seem 
to  be  as  far  behind  the  mirror  as  the  correspond/ 


488  REFLECTION  OF  LIGHT. 

ing  point  of  the  object  is  in  front  of  the  mirror, 
Hence,  images  seen  in  still,  clear  water  are  inverted. 

(a.)  In  Fig.  330,  let  A  represent  a  luminous  point ;  MM,  a  mirror  ; 
A  A'  and  BG,  lines  perpendicular  to  the  mirror.  Rays  from  A  enter 
the  eye  at  DD'.  The  angle  ABC  =  the  angle  CBD  (§656).  The 
angle  ABC  =  the  angle  BAA  (Olney's  Geometry,  Art.  150).  There 
fore  the  angle  CBD  =  the  angle  BAA ' .  The  angle  CBD  =  the  angle 
BA'A  (Olney,  152).  Therefore  the  angle  BAA  =  the  angle  BAA. 
Hence  AM—  A' M  (Olney,  287).  In  other  words,  A'  is  as  far  behind 
the  mirror  as  A  is  in  front  of  it. 

(&.)  Place  a  jar  of  water  10  or  15  cm.  back  of  a  pane  of  glass  placed 
upright  on  a  table  in  a  dark  room.  Hold  a  lighted  candle  at  the 
same  distance  in  front  of  the  glass.  The  jar  will  be  seen  by  light 
transmitted  through  the  glass.  An  image  of  the  candle  will  be 
formed  by  light  reflected  by  the  glass.  The  image  of  the  candle 
wi;  be  seen  in  the  jar,  giving  the  appearance  of  a  candle  burning 
in  water.  The  same  effect  may  be  produced  in  the  evening  by  partly 
raising  a  window  and  holding  the  jar  on  the  outside  and  the  candle 
on  the  inside. 

661.  Reflection  of  Rays  from  Plane  Mir- 
rors.— If  the  incident  rays  be  parallel,  the  reflected  rays 
will  be  parallel.     If  the  incident  rays  be  diverging,  the 
reflected  rays  will  be  diverging ;  they  will  seem  to  diverge 
from  a  point  as  fur  behind  the  reflecting  surface  as  their 
source  is  in  front  of  that  surface  (See  Fig.  330).     If  the 
incident  rays  be  converging,  the  reflected  rays  will  be  con- 
verging ;  they  will  converge  at  a  point  as  far  in  front  of 
the  mirror  as  the  point  at  which  they  were  tending  to 
converge  is  behind  the  mirror. 

662.  Construction    for    the    Image    of   a 
Plane  Mirror. — The  position  of  the  image  of  an  object 
may  be  determined  by  locating  the  images  of  several  well- 
chosen  points  in  the  object  and  connecting  these  images. 

(a.}  In  Fig.  331,  let  AB  represent  an  arrow  ;  MN,  the  reflecting 
gurface  of  a  plane  mirror,  and  E  the  eye  of  the  observer.  Froio 


REFLECTION  OF  LIGHT. 


489 


FIG.  331- 


,  draw  Aa  perpendicular  to  MN  and  make  ad  equal  to  Ad.  Then 
will  a  indicate  the  position  of  the  image 
of  A.  From  B,  draw  Bb  perpendicular 
to  MN  and  make  be  equal  to  Be.  Then 
E  will  b  indicate  the  position  of  the  image 
of  B.  By  connecting  a  and  b  we  locate 
the  image  of  AB.  Draw  aE,  bE,  Ao 
and  Bi.  AoE  represents  one  ray  of  the 
cone  of  rays  from  A  that  enters  the  eye  ; 
BiE  represents  one  ray  of  a  similar  cone 
from  B.  Draw  a  similar  figure  on  a 
larger  scale,  representing  the  eye  at  G. 
Test  your  figure  by  seeing  if  the  angle  of  incidence  is  equal  to  the 
angle  of  reflection.  In  all  such  constructions,  represent  the  direction 
of  the  rays  by  arrow-heads,  as  shown  in  Fig.  331. 

663.  Multiple  Images. — By  placing  two  mirrors 
facing  each  other,  we  may  produce  multiple  images  of 
an    object    placed  between   them.      Each   image  acts 
tt,s    a    material    object    with    respect   to    the    other 
'mirror,  in  which    we    see    an   image   of  the  first 
image.    "When  the  mirrors  are  placed  so  as  to  form  an 
angle  with  each  other,  the  number  of  images  becomes 
limited,  being  one  less  than  the  number  of  times  that  the 
included  angle  is  contained  in   four 

right  angles.  The  mirrors  will  give 
three  images  when  placed  at  an  angle 
of  90°;  five  at  60°;  seven  at  45°. 

(a.}  When  the  mirrors  are  placed  at  right 
angles  the  object  and  the  three  images  will 
be  at  the  corners  of  a  rectangle  as  shown  at  a 
A,  a,  a'  and  a". 

664.  Concave    Mirrors.  —  A  spherical    concave 
mirror  may  be  considered  as  a  small  part  of  a  spherical 
shell  with  its  inner  surface  highly  polished.     Let  MN  (Fig. 
333)  represent  the  section  of  such  a  concave  spherical  mir- 


490  REFLECTION  OF  LIGHT. 

ror,  and  C  the  centre  of  the  corresponding  sphere.  C  is  called 
the  centre  of  curvature  ;  A  is  the  centre  of  the  mirror.  A 
straight  line  of  indefinite  length  drawn  from  A  through 
(7,  as  A  CX,  is  called  the  principal  axis  of  the  mirror.  A 
straight  line  drawn  from  any  other  point  of  the  mirror 
through  C,  as 
JCd,  is  called  a 
secondary  axis. 
The  point  F, 
midway  between 

A     and     (7,    is 

11  j  ^        •  FlG- 333' 

called  the  prin- 
cipal focus.    The  distance  AF  is  the  focal  distance  of  the 
mirror  ;  the  focal  distance  is,  therefore,  one-half  the  radius 
of  curvature.     The  angle  MCN  is  called  the  aperture  of 
the  mirror. 

(a.)  A  curved  surface  may  be  considered  as  made  up  of  an  infinite 
number  of  small  plane  surfaces.  Thus,  a  ray  of  light  reflected  from 
any  point  on  a  curved  mirror  may  be  considered  as  reflected  from  a 
plane  tangent  to  the  curved  surface  at  the  point  of  reflection.  This 
reflection  then  takes  place  in  accordance  with  the  principles  laid 
down  in  §  656.  It  should  be  borne  in  mind  that  the  radii  drawn 
from  C  to  points  in  the  mirror  as  /  and  J  are  perpendicular  to  the 
mirror  at  these  points.  Thus,  the  angles  of  incidence  and  reflection 
for  any  ray  may  be  easily  determined. 

665.  Effect  of  Concave  Mirrors. — The  ten- 
clency  of  ou  concave  jnirror  is  to  increase  the  con- 
vergence or  to  decrease  the  divergence  of  incident 
rays. 

(a.)  If  the  divergence  be  that  of  rays  issuing  from  the  principal 
focus,  the  mirror  will  exactly  overcome  it  and  reflect  them  as  par- 
allel rays.  If  the  divergence  be  greater  than  this,  viz.,  that  of  rays 
issuing  from  a  point  nearer  the  mirror  than  the  principal  focus,  the 
mirror  cannot  wholly  overcome  the  divergence,  but  will  diminish  it 


REFLECTION  OF  LIGHT  491 

The  reflected  rays  will  still  diverge,  but  not  so  rapidly  as  the  incident 
rays.  If  the  divergence  be  less  than  that  first  mentioned,  viz.,  that 
of  rays  issuing  from  a  point  further  from  the  mirror  than  the  prin- 
cipal focus,  the  divergence  will  be  changed  to  convergence  and  a 
peal  focus  will  be  formed. 

666.  The  Principal  Focus.— The  focus  of  a  con- 
cave mirror  is  the  point  toward  which  the  reflected  rays 
converge.     All  incident  rays  parallel  to  the  principal  axis 
will,  after  reflection,  converge  at  the  principal  focus.     The 
principal' focus  is  the  focus  of  rays  parallel  to  the 
principal  axis.    The  rays  will  be  practically  parallel 
when  their  source  is  at  a  very  great  distance,  e.  g.,  the  sun's 
rays.     Solar  rays  coming  to  the  human  eye  do  not  diverge 
a  thousandth  of  an  inch  in  a  thousand  miles. 

(a.)  Above  we  stated  that  parallel  rays  would  be  made  to  converge 
at  the  principal  focus  of  a  spherical  concave  mirror.  This  is  only 
approximately  true;  it  is  strictly  true  in  the  case  of  a  parabolic 
mirror.  In  order  that  the  difference  between  the  spherical  and  the 
parabolic  mirror  may  be  reduced  to  a  minimum,  the  aperture  of  a 
spherical  mirror  must  be  small.  The  case  is  somewhat  analogous 
to  the  coincidence  of  a  circular  arc  of  small  amplitude  with  the 
cycloidal  curve  (§  144,  a).  A  source  of  light  placed  at  the  focus  of 
a  parabolic  mirror  will  have  its  rays  reflected  in  truly  parallel  lines. 
The  head  lights  of  railway  locomotives  are  thus  constructed.  Para- 
bolic mirrors  would  be  more  common  if  it  were  not  so  difficult  to 
make  them  accurately. 

667.  Conjugate    Foci.— Rays  diverging  from  a 
luminous  point  in  front  of  a  concave  spherical  mirror  and 
at  a  distance  from  the  mirrcr  greater  than  its  focal  distance, 
will  converge,  after  reflection,  at  another  point.    The  focus 
thus  formed  will  be  in  a  line  drawn  through  the  luminous 
point  and  the  centre  of  curvature.    In  other  words,  if  the 
luminous  point  lie  in  thr  principal  axis,  the  focus  will  also  ; 
if  the  luminous  point  lie  in  any  secondary  axis,  the  focus 
will  lie  in  the  same  secondary  axis.    The  distinction  be- 


492 


REFLECTION  OF  LIGHT. 


fcween  principal  and  secondary  axes  is  almost  wholly  one 
of  convenience.  Rays  diverging  from  B  will  form  a  focus 
at  b.  The  angle  of  incidence  being  necessarily  equal  to  the 


FIG.  334. 

angle  of  reflection,  it  is  evident  that  rays  diverging  from  b 
would  form  a  focus  at  B.  On  account  of  this  relation 
between  two  such  points,  they  are  called  conjugate  foci. 
Therefore,  conjugate  foci  are  two  points  so  related 
that  each  forms  the  image  of  the  other. 

668,  Construction  for  Conjugate  Foci. — In  the  case 
of  concave  mirrors,  to  locate  the  conjugate  focus  of  a  luminous 
point,  it  is  necessary  to  find  the  point  at  which  at  least  two  reflected 
rays  really  or  apparently  intersect.  The  method  may  be  illustrated 
as  follows : 


Fin.  335- 

(1.)  Let  8  (Fig.   335)  represent  the  luminous  point  whose  con- 
jugate focus  is  to  be  located.    It  may  or  may  not  lie  in  the  principal 
axis.     Draw  the  axis  for  the  point  S,  *.«.,  a  line  from  S  through  C\ 
17 


REFLECTION  OF  LIGHT.  493 

the  centre  of  curvature,  to  the  mirror.  This  line  represents  one  ol 
the  infinite  number  of  rays  sent  from  8  to  the  mirror.  As  this 
incident  ray  is  perpendicular  to  the  mirror,  the  reflected  ray  will 
coincide  with  it.  (Angles  of  incidence  and  of  reflection  =  0.)  The 
conjugate  focus  must  therefore  lie  in  a  line  drawn  through  8  and  0. 
Draw  a  line  representing  some  other  ray,  as  Si.  From  i,  the  point 
of  incidence,  draw  the  dotted  perpendicular  iC.  Construct  the 
angle  Cis  equal  to  the  angle  CiS.  Then  will  is  represent  the  direc- 
tion of  the  reflected  ray.  The  focus  must  also  lie  in  this  line.  The 
intersection  of  this  line  with  the  line  drawn  through  8C  marks  the 
position  of  8,  the  conjugate  focus  of  8. 

(2.)  If  the  reflected  rays  be  parallel,  of  course  no  focus  can  be 
formed.  If  they  be  divergent,  produce  them  back  of  the  mirror  as 
dotted  lines  (Fig.  336)  until  they  intersect.  In  this  case  the  focus 
will  be  virtual,  because  the  rays  only  seem  to  meet.  In  the  other 
cases  the  focus  was  real,  because  the  rays  actually  did  meet. 


FIG.  336. 

(3.)  With  a  radius  of  ±cm.,  describe  ten  arcs  of  small  aperture  to 
represent  the  sections  of  spherical  concave  mirrors.  Mark  the 
centres  of  curvature  and  principal  foci,  and  draw  the  principal 
axes.  Find  the  conjugate  foci  for  points  in  the  principal  axis 
designated  as  follows  :  (1.)  At  a  distance  of  1  cm.  from  the  mirror, 
(2 )  Two  cm.  from  the  mirror.  (3.)  Three  cm.  from  the  mirror. 
(4.)  Four  cm.  from  the  mirror.  (5.)  Six  cm.  from  the  mirror. 
Make  five  similar  constructions  for  points  not  in  the  principal  axis. 
Notice  that  each  effect  is  in  consequence  of  the  equality  between 
the  angle  of  incidence  and  the  angle  of  reflection. 

669.   Formation  of  Images. — Concave  mirrors 
give  rise  to  two  kinds  of  images,  real  and  virtual.    After 


494  REFLECTION  OF  LIGHT. 

learning  what  has  been  said  concerning  conjugate,  real  and 
virtual  foci,  the  formation  of  these  images  will  be  easily 
understood.  The  image  of  an  object  is  determined  by 
finding  the  images  of  a  number  of  points  in  the  object. 

67  O.  Construction  for  Real  Images  Formed  by 
Concave  Mirrors. — (1.)  The  method  may  be  illustrated  as 
follows  :  Let  AB  represent  an  object  in  front  of  a  concave  mirror, 
at  a  distance  greater  than  the  radius  of  curvature.  Draw  Ax,  the 
secondary  axis  for  the  point  A.  The  conjugate  focus  of  A  will  lie 
in  this  line  (§  668  [1]).  From  the  infinite  number  of  rays  sent 
from  A  to  the  mirror,  select,  as  the  second,  the  one  that  is 
parallel  to  the  principal  axis.  This  ray,  after  reflection  at  t,  will 
pass  through  the  principal  focus  (§  666).  The  reflected  rays,  t^and 
xA  (secondary  axis  for  A),  will  intersect  at  «,  which  is  the  con- 


FIG.  337- 

jugate  focus  for  A  In  similar  manner,  b,  the  conjugate  focus  for 
B,  may  be  found.  Points  between  A  and  B  will  have  their  con- 
jugate foci  between  a  and  b. 

(2.)  If  the  eye  of  the  observer  be  placed  far  enough  back  of  the 
image  thus  formed  for  all  of  the  image  to  lie  between  the  eye  and 
the  mirror,  it  will  receive  the  same  impression  from  the  reflected 
rays  as  if  the  image  were  a  real  object.  All  of  the  rays  from  any 
point  in  the  object,  as  A,  that  fall  upon  the  mirror,  intersect  after 
reflection  at  a,  the  conjugate  focus.  These  reflected  rays,  after 
intersecting  at  a,  form  a  divergent  pencil.  A  cone  of  these  rays 
thus  diverging  from  a  enters  the  eye.  They  originally  diverged 


REFLECTION  OF  LIGHT. 


495 


from  A,  but  as  they  enter  the  eye,  they  diverge  from  a.  Hence  the 
effect  produced  (§  659). 

(3.)  From  the  similar  triangles,  ABC  and  dbC,  it  is  evident  that 
the  linear  dimensions  of  the  object  and  of  its  image  are  directly 
proportional  to  their  distances  from  the  centre  of  curvature.  It 
may  also  be  proved  that  the  length  of  the  object  is  to  the  length  of 
the  image  as  the  distance  of  t^ie  object  from  the  principal  focus  is 
to  the  focal  distance  of  the  mirror. 

(4.)  Since  the  lines  that  join  corresponding  points  of  object  and 
image  cross  at  the  centre  of  curvature,  the  real  images  formed  by 
concave  mirrors  are  always  inverted. 


FIG.  338. 

671.  Projection  of  Real  Images  by  Con- 
cave Mirrors. — The  real  image  formed  by  a  concave 
mirror  may  be  rendered  visible  even  when  the  eye  of  the 
observer  is  not  in  the  position  mentioned  in  the  last  article, 
by  projecting  it  upon  a  screen.  In  a  darkened  room,  let  a 
candle  flame  be  placed  in  front  of  a  concave  mirror,  at  a 
distance  from  it  greater  than  the  focal  distance.  Incline 
the  mirror  so  that  the  flame  shall  not  be  on  the  principal 
axis.  Place  a  paper  screen  at  the  conjugate  focus  of  any 


496  REFLECTION  OF  LIGHT. 

point  in  the  luminous  object.  The  proper  position  for  the 
screen  may  easily  be  found  by  trial.  Shield  the  screen  from 
the  direct  rays  of  the  flame  by  a  card  painted  black.  The 
inverted  image  may  be  seen  by  a  large  class.  If  the  image 
fall  between  the  mirror  and  the  candle,  the  screen  should 
be  quite  small.  (See  First  Principles,  Fig.  205.) 

672.  Description  of  Real  Images  Formed 
by  Concave  Mirrors. — (1.)  If  the  object  be  at  the 
principal  focus  there  will  be  no  image.  Why  ?  (You  can 
find  out  by  trying  a  construction  for  the  image  (§  670). 
(2.)  If  the  object  be  between  the  principal  focus  and  the 
centre  of  curvature,  the  image  will  be  beyond  the  centre, 
inverted  and  enlarged.  The  nearer  the  object  is  to  the  prin- 
cipal focus,  the  larger  and  the  further  removed  the  image 
will  be.  (3.)  When  the  object  is  at  the  centre,  the  image 
is  inverted,  of  the  same  size  as  the  object  and  at  the  same 
distance  from  the  mirror.  (4.)  When  the  object  is  not 
very  far  beyond  the  centre  of  curvature,  the  image  will 
be  inverted,  smaller  than  the  object,  and  between  the 
centre  and  the  principal  focus.  (5.)  When  the  object  is 
at  a  very  great  distance,  all  of  the  rays  will  be  practically 
parallel ;  there  will  be  but  one  focus,  and  consequently  no 
image. 

(a.)  For  each  of  these  five  cases  construct  the  images.  The  third 
case  may  be  prettily  illustrated  as  follows :  In  front  of  the  mirror, 
at  a  distance  equal  to  the  radius  of  curvature,  place  a  box  that  is 
open  on  the  side  toward  the  mirror.  Within  this  box  hang  an 
inverted  bouquet  of  bright-colored  flowers.  The  eye  of  the  observer 
is  to  be  in  the  position  mentioned  in  §  670  (2).  By  giving  the  mirror 
a  certain  inclination,  easily  determined  by  trial,  an  image  of  the 
invisible  bouquet  will  be  seen  just  above  the  box.  A  glass  vase 
may  be  placed  upon  the  box  so  that  it  may  seem  to  hold  the  imaged 
flowers. 


REFLECTION  OF  LIGHT.  497 

673.  Construction  for  Virtual  Images  formed  by 
Concave  Mirrors.— Let  AB  represent  an  object  in  front  of  a 
concave  mirror  at  a  distance  from  it  less  than  the  focal  distance. 
Draw  the  secondary  axes  for  the  points  A  and  B,  and  produce  them 
back  of  the  mirror  as  dotted  lines.  From  A  and  B,  draw  the  inci- 
dent rays  Ao  and  Bi,  parallel  to  the  principal  axis.  After  reflection 
they  will  pass  through  the  principal  focus  (§  666).  Produce  these 
rays  back  of  the  mirror  as  dotted  lines  until  they  intersect  tl  3 
prolongations  of  the  secondary  axes  at  a  and  b,  which  will  be  tha 
virtual  conjugate  foci  for  A  and  B.  The  conjugate  foci  for  other 
points  in  AB  will  be  between  a  and  b.  Therefore,  if  the  object  be 
between  the  principal  focus  and  the  mirror,  the  image  will  be 
virtual,  erect  and  enlarged. 


FIG.  339- 

674.  Images  of  the  Observer  formed  by  a 
Concave  Mirror.— A  person  at  a  considerable  distance 
before  a  concave  mirror,  sees  his  image,  real,  inverted  and 
smaller  than  the  object.  As  he  approaches  the  centre  of 
curvature,  the  image  increases  in  size.  As  the  observer 
moves  from  the  centre  to  the  principal  focus,  the  image  is 
formed  back  of  him  and  is,  therefore,  invisible  to  him.  As 
he  moves  from  the  principal  focus  toward  the  mirror,  the 
image  becomes  virtual,  erect  and  magnified,  but  gradually 
growing  smaller.  The  eye  will  not  always  recognize  real 
images  as  being  in  front  of  the  mirror.  It  may  some- 


498         .  REFLECTION  OF  LIGHT. 

times  be  aided  in  this  respect  by  extending  the  outspread 
fingers  between  the  image  and  the  mirror. 

675.  Convex  Mirrors. —  In  convex  mirrors,  the 
foci  are  all  virtual;  the  images  are  virtual,  erect  and 
smaller  than  their  objects.  The  foci  may  be  found  and 
the  images  determined  by  the  means  already  set  forth. 
The  construction  is  made  sufficiently  plain  by  Fig.  340. 


FIG.  340. 

Note.— In  constructions  for  curved  mirrors,  we  have  chosen  two 
particular  rays  for  each  focus  sought ;  one  perpendicular  to  the 
mirror,  the  other  parallel  to  the  principal  axis.  This  was  only  for 
the  sake  of  convenience.  Any  two  or  more  incident  rays  might 
have  been  taken  and  the  direction  of  the  reflected  rays  determined 
by  making  the  angle  of  reflection  equal  to  the  angle  of  incidence. 

EXERCISES. 

1.  What  must  be  the  angle  of  incidence  that  the  angle  between 
jhe  incident  and  the  reflected  rays  shall  be  a  right  angle  ? 

2.  The  radius  of  a  concave  mirror  is  18  inches.     Determine  the 
conjugate  focus  for  a  point  on  the  principal  axis,  12  inches  from 
the  mirror. 

3.  (a.}  Illustrate  by  a  diagram  the  image  of  an  object  placed  at  the 
principal  focus  of  a  concave  mirror;   (&.)  of  one  placed  between 
that  focus  and  the  mirror  ;  (c.)  of  one  placed  between  tjie  focus  and 
the  centre  of  the  inirrpr. 


REFLECTION  OF  LIGHT.  499 

4.  (a.)  What  kind  of  mirror  always  makes  the  image  smaller  than 
the  object?     (6.)  What  kind  of  a  mirror  may  make  it  larger  or 
smaller,  and  according  to  what  circumstances  ? 

5.  Rays  parallel  to  the  principal  axis  fall  upon  a  convex  mirror. 
Draw  a  diagram  to  show  the  course  of  the  reflected  rays. 

6.  (a.)  Why  do  images  formed  by  a  body  of  water,  appear  in- 
verted?   (6.)  What  is  the  general  effect  of  concave  mirrors  upon 
incident  rays  ? 

7.  A  person,  placed  at  a  considerable  distance  before  a  concave 
mirror,  sees  his  image,    (a.)  How  does  it  appear  to  him  ?    He  ap 
preaches  the  mirror  and  the  image  changes.    (&.)   Describe  the 
changes  that  take  place  until  he  sees  a  virtual  image  of  himself. 

8.  A  man  stands  before  an  upright  plane  mirror  and  notices  that 
he  cannot  see  a  complete  image  of  himself.    («.)  Could  he  see  a 
complete  image  by  going  nearer  the  mirror?     Why  ?    (6.)  By  going 
further  from  it  ?    Why  ? 

9.  When  the  sun  is  30°  above  the  horizon,  its  image  is  seen  in  a 
tranquil  pool.     What  is  the  angle  of  reflection  ? 

10.  A  person  stands  before  a  common  looking-glass  with  the  left 
eye  shut.    He  covers  the  image  of  the  closed  eye  with  a  wafer  on 
the  glass.     Show  that  when,  without  changing  his  position,  he 
opens  the  left  and  closes  the  right  eye,  the  wafer  will  still  cover  the 
image  of  the  closed  eye. 

11.  The  distance  of  an  object  from  a  convex  mirror  is  equal  to  the 
radius  of  curvature.     Show  that  the  length  of  the  image  will  be 
one-third  that  of  the  object. 

Recapitulation. — In  this  section  we  have  considered 
the  Nature  and  Laws  of  Reflection;  Dif- 
fused and  Invisible  light;  the  Apparent  Direc- 
tion of  bodies;  Images  formed  in  Plane  Mirrors 
and  their  Construction  ;  Concave  Mirrors, 
their  Effects,  Principal  and  Conjugate  Foci ; 
Images  formed  by  them  with  their  Construction, 
Projection  and  Description;  foci  and  images  for 
Convex  Mirrors, 


500 


REFRACTION  OF  LIGHT. 


HI. 


REFRACTI  ON    OF    LIGHT 

(>76.  Preparatory.  —  So  far,  we  have  considered  only 
that  part  of  the  incident  beam  that  is  turned  back  from 
the  reflecting  surface.  As  a  general  thing,  a  part  of  the 
beam  enters  the  reflecting  substance,  being  rapidly  absorbed 
when  the  substance  is  opaque  and  freely  transmitted  when 
the  substance  is  transparent.  We  have  now  to  consider 
those  rays  that  enter  a  transparent  substance. 

(a.)  Procure  a  clear  glass  bottle  with  flat  sides,  about  4  inches 
(10  cm.}  broad.  On  one  side  paste  a  piece  of  paper,  in  which  a  circu- 
lar hole  has  been  cut.  On 
this  clear  circular  space, 
draw  two  ink-marks  at 
right  angles  to  each 
other,  as  shown  in  Fig. 
341.  Fill  the  bottle  with 
clear  water  up  to  the 
level  of  the  horizontal 
ink-mark.  Hold  it  so 
that  a  horizontal  sun- 
beam from  the  heliostat 
may  pass  through  the 
clear  sides  of  the  bottle 
above  the  water,  and  no- 
tice that  the  beam  passes 
through  the  bottle  in  a 
straight  line.  Raise  the 
bottle  so  that  the  beam 
shall  pass  through  the 
water,  and  notice  that  the 
beam  is  still  straight. 
In  a  card,  cut  a  slit  about 

5  cm.  long  and  1  mm.  wide.     Place  the  card  against  the  bottle  as 
shown  in  the  figure.    Reflect  the  beam  through  this  slit  so  that  it 


Fia  34  » 


REFRACTION  OF  L1G8T. 


501 


shall  fall  upon  the  surface  of  the  water  at  i,  the  intersection  of  the 
two  ink-marks.  Notice  that  the  reflected  beam  is  straight  until  it 
reaches  the  water,  but  that  it  is  bent  as  it  obliquely  enters  the 
water. 

677.  Refraction. — Refraction   of  light   is   the 
bending  of  cu  luminous  ray  when  it  passes  from 
^ne  medium  to  another. 

678.  Index  of  Refraction. — If  a  ray  of  light  from 
L  (Fig.  342)  fall  upon  the  surface  of  water  at  A,  it  will  be 
refracted  as  shown  in  the  figure.     The  angle  LAS  is  the 
angle  of  incidence  and  KAC  the  angle  of  refraction,  BC 
being  perpendicular  to  the  water's  surface.     From  A  as  a 

centre,  with  a  radius  equal  to  unity, 
describe  a  circle.  From  the  points  m 
and  p,  where  this  circle  cuts  the  inci- 
dent and  refracted  rays,  draw  mn  and 
pq  perpendicular  to  BC.  Then  will 
mn  be  the  sine  of  the  angle  of  incidence 
SLudipq  the  sine  of  the  angle  of  refrac- 
tion. The  quotient  arising  from 
dividing  the  sine  of  the  angle  of 
incidence  by  the  sine  of  the  angle  of  refraction  is 
called,  the  index  of  refraction  for  the  two  media. 
It  is  evident  that  the  greater  the  refractive  power  of  the 
substance,  the  less  the  value  of  the  divisor  pq,  and  the 
greater  the  value  of  the  quotient,  the  index  of  refrac- 
tion. 

(a.)  The  following  table  gives  the  indices  of  refraction  when  light 
passes  from  a  vacuum  into  any  of  the  substances  named  : 

Flint  glass 1.575 


FIG  342. 


Mr 1.000294 

Water 1.336 

Alcohol 1374 

Crown  glass 1.534 


Carbon  bisulphide 1.678 

Diamond 2.439 

Lead  chromate .2.974 


502 


REFRACTION  OF  LIGHT. 


The  index  of  refraction  for  any  two  media  may  be  found  by  divid- 
ing the  absolute  index  of  one,  as  given  above,  by  the  absolute  index 
of  the  other. 

679.  Laws    of   Refraction    of   Light.  — (1.) 

When  light  passes  perpendicularly  from  one  me* 
dium  to  another  it  is  not  refracted. 

(2.)  When  light  passes  obliquely  from  a  rarer  to 
a  denser  medium  it  is  refracted  toward  a  line  drawn,  at 
the  point  of  incidence,  perpendicular  to  the  refracting 
surface,  or,  more  briefly,  it  is  refracted  toward  the 
perpendicular. 

(3.)  W^^en  light  passes  obliquely  from  a  denser 
to  a  rarer  medium,  it  is  refracted  from  the  per- 
pendicular. 

(4.)  The  incident  and  refracted  rays  are  in  the  same 
plane  which  is  perpendicular  to  the  refracting  surface. 

(5.)  The  index  of  refraction  is  constant  for  the  same  two 
media. 

680.  Illustrations  of  Refraction.— Put  a  small  coin  into 
a  tin  cup  and  place  the 

cup  so  that  its  edge  just 

intercepts  the  view  of 

the  coin.    A  ray  of  light 

coming  from   the   coin 

toward     the     observer 

must  pass  above  his  eye 

and    thus    be    lost   to 

sight.    If,  now,  water  be 

gradually    poured    into 

the  cup,  the  coin  will 

become     visible.      The 

rays  are  bent  down  as 

they  emerge   from  the 

water  and  some  of  them  FIG.  343. 

enter  the  eye.    For  the 

same  reason,  an  oar  or  other  stick  half  immersed  in  water  seems 

bent  at  the  water's  surface,  while  rivers  and  ponds  whose  bottoms 


REFRACTION  OF  LIGHT. 


503 


are  visible  are  generally  deeper  than  they  seem  to  be.  (Fig.  343.) 
As  air  expands,  its  index  of  refraction  becomes  less.  Hence  the 
indistinctness  and  apparent  unsteadiness  of  objects  seen  through 
air  rising  from  the  surface  of  a  hot  stove.  Light  is  refracted  as  it 
enters  the  earth's  atmosphere.  Hence  the  heavenly  bodies  appear 
to  be  further  above  the  horizon  than  they  really  are  except  when 
they  are  overhead. 

681.  Total  Reflection.  — When  a  ray  of  light 
passes  from  a  rarer  into  a  denser  medium,  it  may  always 
approach  the  perpendicular  so  as  to  make  the  angle  of  re- 
fraction less  than  the  angle  of  incidence  (§  679  [2]).  But 
when  a  ray  of  light  attempts  to  pass  from  a  denser  into  a 
rarer  medium  there  are  conditions 
under  which  the  angle  of  refraction 
cannot  be  greater  than  the  angle  of 
incidence.  Under  such  circum- 
stances the  ray  cannot  emerge 
from  the  denser  medium,  but 
will  be  wholly  reflected  at  the 
point  of  incidence.  Fig.  344  represents  luminous  rays 
emitted  from  A,  under  water,  and  seeking  a  passage  into 
air.  Passing  from  the  perpendicular,  the  angle  of  refrac- 
tion increases  more  rapidly  than  the  angle  of  incidence 
until  one  ray  is  found  that  emerges  and  grazes  the  surface 
of  the  water.  Eays  beyond 
this  cannot  emerge  at  all. 


683.  The  Critical  An- 
gle. —  Imagine  a  spherical 
(Florence)  flask  half  filled 
with  water.  A  ray  of  light 
from  L  will  be  refracted  at  A 
in  the  direction  of  R.  If  the 
angle  of  incidence,  GAL,  be 


FIG.  344 


FIG.  345. 


504  REF&AC'HOX  OF  LIG&T. 

gradually  increased  the  angle  of  refraction  will  be  gradually 
increased  until  it  becomes  90°,  when  the  ray  will  graze  the 
surface  of  the  water  AM.  If  the  source  of  light  be  still 
further  removed  from  (7,  as  to  I,  the  ray  will  be  reflected 
to  r  (§  656).  For  all  media  there  is  an  incident  angle  of 
this  kind,  called  the  critical  or  limiting  angle,  beyond 
which  total  internal  reflection  will  take  the  place  of  refrac- 
tion. The  reflection  is  called  total  because  all  of  the 
incident  light  is  reflected,  which  is  never  the  case  in 
ordinary  reflection.  Hence,  a  surface  at  which  total  re- 
flection takes  place  constitutes  the  most  perfect  mirror 
possible.  The  critical  angle  (with  reference  to  air)  is 
48°  35'  for  water;  40°  49'  for  glass;  23°  43'  for  diamond. 

(a.)  From  this  it  follows,  as  may  be  seen  by  referring  to  Fig.  344, 
that  to  an  eye  placed  under  water,  all  visible  objects  above  the 
water  would  appear  within  an  angle  of  97°  10',  or  twice  the  critical 
angle  for  water. 

(&.)  The  phenomena  of  total  reflection  may  be  produced  by  placing 
the  bottle  shown  in  Fig.  341  upon  several  books  resting  upon  a  table, 
and  inverting  the  card  so  that  a  beam  of  light  reflected  obliquely 
upward  from  a  mirror  on  the  table  may  enter  through  the  slit  near 
the  bottom  of  the  bottle,  taking  a  direction  through  the  water  simi- 
lar to  the  line  I A  of  Fig.  345.  When  one  looks  into  an  aquarium  in 
a  direction  similar  to  rA,  images  of  fish  or  turtles  near  the  surface 
of  the  water  are  often  seen. 

(c.)  Place  a  strip  of  printed  paper  in  a  test-tube ;  hold  it  ob- 
liquely in  a  tumbler  of  water  and  look  downward  at  the  printing 
which  will  be  plainly  visible.  Change  the  tube  gradually  to  a 
vertical  position,  and  soon  the  part  of  the  tube  in  the  water  takes  a 
silvered  appearance  and  the  printing  becomes  invisible.  Show  that, 
in  this  case,  the  disappearance  of  the 
reading  is  due  to  total  reflection.  By 
dissolving  a  small  bit  of  potassium  di- 
chromate  in  the  water,  the  tube  will 
have  a  golden  instead  of  a  silver-like 
appearance. 

(d.)  Fig.  346  represents  a  glass  vessel 
partly  filled  with   water.      Mirrors    are  FIG.  346. 


REFRACTION  OF  LIGHT. 


505 


placed  at  m  and  n. 
and  refracted  at  i. 


In  this  way  a  ray  may  be  reflected  at  m,  n  and  0, 


(e.)  Fig.  347  represents  a  glass  jar  with  an  opening,  from  which 

a  stream  of  water  issues  under  a 
head  (§  254  [«])  kept  constant. 
Through  a  lens  placed  opposite 
this  orifice,  a  concentrated  beam 
of  light  from  the  heliostat  is 
thrown  into  the  stream  of  water 
as  it  issues.  Internal  reflection 
keeps  most  of  it  there,  a  prisoner. 
The  stream  of  water  is  full  of 
light  and  appears  a  stream  of 
melted  metal.  Thrust  a  finger 
into  the  stream  and  notice  the 
effect.  Place  a  piece  of  red  gluss 
between  the  heliostat  and  the 
lens  ;  the  water  looks  like  blood. 


FIG.  347. 


Thrust  the  finger  into  the  stream  again.     Repeat  the  experiment 
with  pieces  of  glass  of  other  colors  in  place  of  the  red. 

683.  Refraction  Explained.— To  understand  the 
way  in  which  a  ray  of  light  is  refracted,  let  us  consider  its 
passage  through  a  glass  prism,  ABC.  It  must  be  under- 
stood that  the  velocity  of  light  is 
less  in  glass  than  in  air,  and 
that  the  direction  in  which  a 
ivave  moves  is  perpendicular  to 
its  wave  front.  A  wave  in  the 
ether  approaches  the  surface  of  the 
prism  AB.  When  at  a,  the  lower  end  of  the  wave  front 
first  strikes  the  glass  and  enters  it.  The  progress  of  this 
end  of  the  wave  front,  being  slower  than  that  of  the  other 
which  is  still  in  the  air,  is  continually  retarded  until  the 
whole  front  has  entered  the  glass.  The  wave  front  thus 
assumes  the  position  shown  at  c.  But  the  path  of  the 
wave  being  perpendicular  to  the  front  of  the  wave,  this 


FIG.  348. 


R&F&ACTION  OP 


change  of  front  causes  a  change  in  the  direction  of  the  ray 
which  is  thus  refracted  toward  a  perpendicular.  The  wave 
now  moves  forward  in  a  straight  line  until  the  top  of  the 
wave  front  strikes  A  C,  the  surface  of  the  prism,  as  shown 
at  m.  The  upper  end  of  the  wave  front  emerging  first 
into  the  air  gains  upon  the  other  end  of  the  front  which  is 
still  moving  more  slowly  in  the  glass.  When  the  lower 
end  emerges  from  the  glass,  the  wave  has  the  position 
shown  at  n.  This  second  change  of  front  involves  another 
change  in  the  direction  of  the  ray  which  is  now  refracted, 
from  the  perpendicular.  (See  First  Principle*,  §  443,  a.  ) 

684.  Three  Kinds  of  Refractors.—  When  a  ray 

of  light  passes  through  a  refracting  medium,  three  cases 
may  arise  : 

(1.)  When  the  refractor  is  bounded  by  planes,  the  re- 
fracting surfaces  being  parallel. 

(2.)  When  the  refractor  is  bounded  by  planes,  the  re- 
fracting surfaces  being  not  parallel.  The  refractor  is  then 
called  a  prism. 

(3.)  When  the  refractor  is  bounded  by  two  surfaces  of 
which  at   least    one   is 
curved.      The  refractor 
is  then  called  a  lens. 

685.  Parallel 
Plates.  —  When  a  ray 
passes   through    a   me- 

dium bounded  by  paral- 

FIG.  349. 
lei  planes  the  refractions 

at  the  two  surfaces  are  equal  and  contrary  in  direction, 
The  direction  of  the  ray  after  passing  through  the  plate  is 


OP  LIGHT.  50? 

parallel  to  its  direction  before  entering;  the  ray  merely 
suffers  lateral  aberration.  Objects  seen  obliquely  through 
such  plates  appear  slightly  displaced  from  their  true  position. 

686.  Prisms. — A  prism  produces  two  simultaneous 
effects  upon  light  passing  through  it ;  a  change  of  direc- 
tion and  decomposition.  The  second  of  these  effects  will 
be  considered  under  the  head  of  dispersion  (§  701). 

(a.)  Let  mno  represent  a  section  formed  by  cutting  a  prism  by  a 
plane  perpendicular  to  its  edges.     A  ray  of  light  from  L  being  re- 
fracted at  a  and  &  en 
ters  the  eye  in  the  di- 
rection be.     The  object 
being  seen  in  the  direc- 
tion of  the  ray  as  it 
enters  the  eye  (§  659), 
appears  to  be  at  r.    An 
object  seen  through  a 
prism    seems     to     be 
moved  in  the  direction 
of  the  edge  that  sepa- 
rates    the     refracting 
surfaces.      The     rays  FIG.  350. 

themselves     are    bent 

toward  the  side  that  separates  the  refracting  surfaces,  or  toward 
the  thickest  part  of  the  prism. 

(&.)  Prisms  are  generally  made  of  glass,  their  principal  sections 
being  equilateral  triangles.  In  order  to  give  a 
liquid  the  form  of  a  prism,  it  is  placed  in  a 
vessel  (Fig.  351)  in  which  at  least  two  sides 
are  glass  plates  not  parallel.  Bottles  are  made 
for  this  purpose. 

(c.)  In  Fig.  352,  ABC  is  the  principal  section 
of  a  right-angled  isosceles,  glass 
FIG.  351.  prism,  right-angled  at  G.     A  ray 

of  light  falling  perpendicularly 
npon  either  of  the  cathetal  (cathetus)  surfaces,  as  AC, 
will  not  be  refracted.     With  AB,  it  will  make  an 
angle  of  45°  which  exceeds  the  critical  angle   for 
glass  (§  682).     It  will  therefore  be  totally  reflected         'IG'  352' 
and  pass  without  refraction  from  the  cathetal  surface  BC.     Such 
prisms  are  often  used  in  optics  instead  of  mirrors. 


508 


REFRACTION  OF  LIGHT. 


687.  Lenses. — Lenses  are  generally  made  of  crown 
glass  which  is  free  from  lead,  or  of  flint  glass  which  con- 
tains lead  and  has  greater  refractive  power.  The  curved 
surfaces  are  generally  spherical.  "With  respect  to  their 
shape,  lenses  are  of  six  kinds : 
123 


Thinner  at  the  middle  than 
at  the  edges. 


FIG.  353- 

(1.)  Double-convex,  |  Thicker  at  the  middle 

(2.)  Plano-convex,  at  the  edges. 

(3.)  Concavo-convex,  or  meniscus,  J 

The  double-convex  may  be  taken  as  the  type  of  these. 

(4.)  Double-concave,  "| 

(5.)  Plano-concave, 
(6.)  Convex-concave,  or  diverging  j 
meniscus,  J 

The  double-concave  may  be  taken  as  the  type  of  these. 
(a.)  The  effect  of  convex  lenses  may  be  considered  as  produced  by 
two  prisms  with  their  bases  in  contact ;  that  of  concave  lenses,  by 
two  prisms  with  their  edges  in  contact. 

688.  Centre  of  Curvature ;  Principal  Axis ; 
Optical  Centre. — A  double-convey  lens  may  be  de- 
scribed as  the  part  common  to  two  spheres  which  intersect 
each  other.  The  centres  of  these  spheres  are  the  centres 
of  curvature  of  the  lens.  The  straight  line  passing 
through  the  centres  of  curvature  is  the  principal  axis  of 
the  lens.  In  every  lens  there  is  a  point  on  the  principal 
axis  called  the  optical  centre.  When  the  lens  is  bounded 
by  spherical  surfaces  of  equal  curvature,  as  is  generally  the 
case,  the  optical  centre  is  at  equal  distances  from  the  two 


REFRACTION  OF  LIGHT.  509 

faces  of  the  lens.  Any  straight  line,  other  than  the  prin- 
cipal axis,  passing  through  the  optical  centre  is  a  second- 
ary axis.  (See  First  Principles,  Fig.  216.) 

(a.)  If  a  ray  of  light  passing  through  the  optical  centre  be  re- 
fracted at  all,  the  two  refractions  will  be  equal  and  opposite  in  direc 
tion.  The  slight  lateral  aberration  thus  produced  may  be  disregarded, 

689.  Principal  Focus. — Ml  rays  parallel  to 
the  principal  axis  will,  after  two  refractions,  con- 
verge at  a  point  called  the  principal  focus.  This 
point  may  lie  on  either  side  of  the  lens,  according  to  the 
direction  in  which  the  light  moves ;  it  is  a  real  focus.  The 
greater  the  refracting  power  of  the  substance  of  which  the 


FIG.  354- 

lens  is  made,  the  nearer  the  principal  focus  will  be  to  the 
Jens.  In  a  double-convex  lens  of  crown  glass,  the  principal 
focal  distance  is  equal  to  the  radius  of  curvature;  in  a 
plano-convex  lens  of  the  same  material,  it  is  twice  as  great. 

(a.)  The  position  of  the  principal  focus  of  a  lens  is  easily  deter- 
mined. Hold  the  lens  facing  the  sun.  The  parallel  solar  rays 
incident  upon  the  lens  will  converge  at  the  principal  focus.  Find 
this  point  by  moving  a  sheet  of  paper  back  and  forth  behind  the 
lens  until  the  bright  spot  formed  upon  the  paper  is  brightest  and 
smallest.  (See  First  Prin.  Nat.  Phil.,  Exp.  228.) 

(b.)  It  is  also  true  that  rays  diverging  from  a  point  at  twice  the 
principal  focal  distance  from  the  lens  will  converge  at  a  point  just 
as  far  distant  on  the  other  side  of  the  lens.  Rays  diverging  from 
/  will  converge  at  /',  these  two  points  being  at  twice  the  focal  dis- 
tance from  the  lens.  By  experimenting  with  a  lens  and  candle- 
flame  until  the  flame  and  its  image  are  at  equal  distances  from  the 
lens,  we  are  able,  in  a  second  way,  to  determine  the  principal  focal 
distance  of  the  lens.  The  conjugate  foci  situated  at  twice  the  prin- 
cipal focal  distance  aye  called  secondary  foci. 


510  REFRACTION  OF  LIGHT. 

69O.  Conjugate  Foci.— Kays  diverging  from  a 
luminous  point  in  the  principal  axis  at  a  small  distance 
beyond  the  principal  focus  on  either  side  of  the  lens  will 
form  a  focus  on  the  principal  axis  beyond  the  other  prin- 
cipal focus.  Thus,  rays  from  L  will  converge  at  /;  con- 
versely, rays  from  /  will  converge  at  L  (§  667).  If  the 
luminous  point  be  in  a  secondary  axis,  the  rays  will  con- 
verge to  a  point  in  the  same  secondary  axis.  Two 


FIG.  355- 

points  thus  related  to  each  other  are  called  con- 
jugate foci;  the  line  joining  them  always  passes 
through  the  optic-al  centre. 

(a.)  If  the  luminous  point  be  more  than  twice  the  focal  distance 
from  the  lens,  the  conjugate  focus  will  lie  on  the  other  side  of  the 
lens  at  a  distance  greater  than  the  focal  distance,  but  less  than  twice 
the  focal  distance.  If  the  luminous  point  be  moved  toward  the 
lens,  the  focus  will  recede  from  the  lens.  When  the  luminous 
point  is  at  one  secondary  focus,  the  rays  will  converge  at  the  other 
secondary  focus.  When  the  luminous  point  is  between  the  second- 
ary and  principal  foci,  the  rays  will  converge  beyond  the  secondary 
focus  on  the  other  side  of  the  lens.  When  the  luminous  point  is  at 
the  focal  distance,  the  emergent  rays  will  be  parallel  and  no  focus 
will  be  formed.  When  the  luminous  point  is  at  less  than  the  focal 
distance,  the  emergent  rays  will  still  diverge  as  if  from  a  point  on 
the  same  $ide  pf  the  lens,  more  distant  than  the  principal  focus 


REFRACTION  OF  LIGHT. 


511 


FIG.  356. 


This  focus  will  be  virtual.  Conversely,  converging  rays  falling 
upon  a  convex  lens  will  form  a  focus  nearer  the  lens  than  the 
principal  focus.  (See  Fig.  356.) 

691.    Conjugate  Foci  of  Concave  Lens.— 

Rays  from  a  luminous  point  at  any  distance  whatever  will 
be  made  more  divergent  by  passing  through  a  concave  lens. 


FIG.  357. 

Rays  parallel  to  the  principal  axis  will  diverge  after  refrac- 
tion as  if  they  proceeded  from  the  principal  focus.  In 
any  case,  the  focus  will  be  virtual,  and  nearer  the  lens  thai) 
the  luminous  point. 

692.  Images  Formed  by  Convex  Lenses.— 

The  analogies  between  the  convex  lens  and  the  concave 


512  REFRACTION  OF  LIGHT. 

mirror  cannot  have  escaped  the  notice  of  the  thoughtful 
pupil.  Others  will  appear.  If  secondary  axes  be  nearly 
parallel  to  the  principal  axis,  well-defined  foci  may  be 
formed  upon  them,  as  well  as  upon  the  principal  axis.  A 
number  of  these  foci  may  determine  the  position  of  an 
image  formed  by  a  lens. 

(a.)  The  linear  dimensions  of  object  and  image  are  directly  as 
their  respective  distances  from  the  centre  of  the  lens  ;  they  will  be 
virtual  or  real,  erect  or  inverted,  according  as  they  are  on  the  same 
side  of  the  lens  or  on  opposite  sides. 

693.  Construction  for  Real  Images.— To  determine 
the  position  of  the  image  of  the  object  AB  (Fig.  358),  draw  from 
any  point,  as  A,  a  line  parallel  to  the  principal  axis.  After  refrac- 


FIG.  358. 

tion,  the  ray  represented  by  this  line  will  pass  through  F,  the  prm- 
cipal  focus.  Draw  the  secondary  axis  for  the  point  A.  The  inter- 
section of  these  two  lines  at  a  determines  the  position  of  the  con- 
jugate focus  of  A.  In  similar  manner,  the  conjugate  focus  of  S  is 
found  to  be  at  &.  Joining  these  points,  the  line  ah  is  the  image  of 
the  line  AB. 

694.  Diminished  Real  Image.— If  the  object 
be  more  than  twice  the  focal  distance  from  the  convex 
lens,  its  image  will  be  real,  smaller  than  the  object  and 
inverted  (Fig.  359).  Construct  the  image  as  indicated  in 
the  last  paragraph. 


REFRACTION  OF  LIGHT. 


513 


FIG.  359. 

695.    Magnified  Real  Image.— If  the  object  be 
further  from  the  lens  than  the  principal  focus,  but  at  a 


FIG.  360. 

distance  less  than  twice  the  focal  distance,  the  image  will 
be  real,  magnified  and  inverted.  (Fig.  360.)  Construct 
the  image. 


514;  REFRACTION  OF  LIGHT. 

696.  Virtual    Image. — If  the  object   be  placed 
nearer  the  lens  than  the  principal  focus,  the  image  will  be 
virtual,  magnified  and  erect.     (Fig.  361.)    This  explains 
the  familiar  magnifying  effects  of  convex  lenses.     Con- 
struct the  image. 

697.  Image  of  Concave  Lens.— Images  formed 
by  a  concave  lens  are  virtual,  smaller  than  the  object  and 
erect.    The  construction  of  the  image  is  shown  in  Fig. 
362. 


FIG.  362. 

* 

Note. — The  power  of  the  convex  lens  to  form  real  and  diminished 
images  of  distant  objects  and  magnified  images  of  near  objects,  is 
of  frequent  application  in  such  optical  instruments  as  the  micro- 
scope, telescope,  magic  lantern,  lighthouse  lamps,  etc.  Owing  to 
the  identity  between  heat  and  luminous  rays,  a  convex  lens  is  also 
a  "  burning-glass." 

698.  Spherical  Aberration. — The  rays  that  pass 
through  a  spherical  lens  near  its  edge  are  more  refracted 
than  those  that  pass  nearer  the  centre.  They,  therefore, 
converge  nearer  the  lens.  A  spherical  lens  cannot  refract 
all  of  the  incident  rays  to  the  same  point.  Hence 
"spherical  aberration"  and  its  annoying  consequences  in 
the  construction  and  use  of  optical  apparatus. 


REFRACTION  OF  LIGHT.  515 


EXERCISES. 

1.  (a.)  What  is  refraction  of  light  ?    (&.)  State  the  laws  governing 
the  same,  and  (c.)  give  an  illustrative  diagram. 

2.  (a.)  Name  and  illustrate  by  diagram  the  different  classes  of 
lenses.     (&.)  Explain,  with  diagram,  the  action  of  the  burning-glass 

3.  (a.)  Explain  the  cause  of   total  reflection.     (&.)   Show,    with 
diagram,  how  the  secondary  axes  of  a  lens  mark  the  limits  of  the 
image. 

4.  (a.)  Using  a  convex  lens,  what  must  be  the  position  of  an 
object  in  order  that  its  image  shall  be  real,  magnified,  and  inverted  1 
(6.)  Same,  using  a  concave  lens  ? 

5.  (a.)  Show  how  a  ray  of  light  may  be  bent  at  a  right  angle  by 
a  glass  prism.     (&.)  The  focal  distance  of  a  convex  lens  being  6 
inches,  determine  the  position  of  the  conjugate  focus  of  a  point 
12  inches  from  the  lens,    (c.)  18  inches  from  the  lens. 

6.  (a.)  The  focal  distance  of  a  convex  lens  is  30  cm.    Find  the 
eonjugate  focus  for  a  point  15  cm.  from  the  lens.     (6.)  How  may  the 
focal  length  of  a  lens  be  determined  experimentally? 

7.  If  an  object  be  placed  at  twice  the  focal  distance  of  a  convex 
lens,  how  will  the  length  of  the  image  compare  with  the  length  of 
the  object  ? 

8.  A  small  object  is  12  inches  from  a  lens  ;  the  image  is  24  inches 
from  the  lens  and  on  the  opposite  side.    Determine  (by  construction) 
the  focal  distance  of  the  lens. 

9.  A  candle  flame  is  6  feet  from  a  wall ;  a  lens  is  between  the 
flame  and  the  wall,  5  feet  from  the  latter.     A  distinct  image  of  the 
flame  is  formed  upon  the  wall,    (a.)  In  what  other  position  may 
the  lens  be  placed,  that  a  distinct  image  may  be  formed  upon  the 
wall ?    (6.)  How  will  the  lengths  of  the  images  compare? 


Recapitulation. — In  this  section  we  have  considered 
the  Definition,  Index,  Laws  and  Explanation 
of  refraction ;  Internal  Reflection ;  Plates, 
Prisms  and  Lenses ;  principal  and  conjugate  Foci 
of  lenses ;  Construction  for  conjugate  foci  and 
images;  Spherical  Aberration. 


516 


CHROMATICS  —  SPECTRA. 


IV. 


CHROMATICS.—  SPECTRA. 

699.  Other  Results  of  Refraction.—  In  our  previous 
<»nsideration  of  luminous  rays  we  have  studied  the  effect  of  refiec 
tion  and  refraction  upon  the  direction  of  rays  ;  in  fact,  we  have 
dealt  with  only  those  properties  which  are  common  to  all  luminous 
rays.  But  the  properties  of  light  and  the  phenomena  of  refraction 
are  not  so  simple  as  we  might  thus  be  led  to  suppose.  Most 
luminous  objects  emit  light  of  several  kinds  blended  together.  We 
must  not  be  satisfied  with  our  knowledge  of  light  until  we  are  able 
to  sift  these  varieties  one  from  the  other,  and  to  deal  with  any  one 
kind  by  itself. 


FIG.  363. 

7OO.  Solar  Spectrum. — Admit  a  sunbeam  through 
a  very  small  opening  in  the  shutter  of  a  darkened  room. 
The  opening  may  be  prepared  by  cutting  a  slit  an  inch 
(25  mm.}  long  and  ^  of  an  inch  (1  mm.)  wide  in  a  card. 
See  that  the  edges  of  the  slit  are  smooth.  Tack  the 
card  over  an  opening  in  the  shutter.  If  we  look  at  the 
aperture  from  E  we  shall  see  the  sun  beyond.  The  path 
of  the  beam  from  8  to  E  is  made  visible  by  the  floating 


CHROMATICS— SPECTRA.  517 

dust.  If  a  prism  be  placed  in  the  path  of  the  beam,  as 
shown  in  Fig.  363,  the  sides  of  the  slit  and  edges  of  the 
prism  being  horizontal,  the  beam  will  be  refracted  upward^ 
If  the  refracted  beam  be  caught  upon  a  screen,  it  will 
appear  as  a  band  of  differently  colored  light,  passing  by 
imperceptible  gradations  from  red  at  the  bottom,  through 
orange,  yellow,  green,  blue  and  indigo  to  violet  at  the 
upper  end  of  the  beautifully  colored  band.  This  colored 
band  is  called  the  solar  spectrum. 

(a.)  The  different  colors  do  not  occupy  equal  space  in  the  spectrum, 
orange  having  the  least  and  violet  the  most.  The  initials  of  these 
colors  form  the  meaningless  word  VIBGYOR,  which  may  aid  the 
memory  in  remembering  these  prismatic  colors  in  their  proper 
order.  By  placing  the  slit  in  a  vertical  position,  and  standing  the 
prism  on  its  end  so  that  its  edges  will  be  parallel  with  the  sides  of 
the  slit,  the  spectrum  will  be  projected  as  a  horizontal  band. 

701.  Dispersion.— By  looking  at  Fig.  363,  it  will 
be  seen  that  the  red  rays  have  been  refracted  the  least  and 
the  violet  the  most  of  all  the  luminous  rays.     This  sepa- 
ration of  the  differently  colored  rays  by  the  prism 
is  called  the  dispersion  of  light ;  it  depends  upon  the 
fact  that  rays  of  different  colors  are  refracted  in  different 
degrees. 

702.  Pure  Spectrum.— The  spectrum  above  de- 
scribed is  composed  of  overlapping  and  differently-colored 
images  of  the  slit.     In  a  pure  spectrum  these  images  must 
not  overlap.    The  first  requisite  in  preventing  this  over- 
lapping is  that  the  slit  be  very  narrow. 

(a.)  The  most  simple  way  of  producing  a  pure  spectrum  is  to  look 
jhrough.  a  prism  at  a  very  narrow  slit  in  the  shutter  of  a  darkened 
room.  The  edges  of  the  prism  should  be  parallel  to  the  slit ;  the 
prism  should  be  at  least  five  feet  (1|  m.)  from  the  slit ;  the  prism 
should  be  Burned  until  the  colored  image  of  the  slit  is  at  the  least 


518  CHS  OMA  TICS — SPECTRA. 

angular  distance  from  the  slit  itself.  A  pure  spectrum  is  also 
obtained  by  passing  the  beam  through  several  prisms  in  succession, 
thus  increasing  the  dispersion. 

7O3.  Fraunhofer's  Lines. — A  pure  solar  spectrum 
is  not  continuous,  but  is  crossed  by  numerous  dark  lines, 
many  hundreds  of  which  have  been  counted  and  accu- 
rately mapped.  The  more  conspicuous  of  these  dark  lines 
are  distinguished  by  letters  of  the  alphabet,  as  shown  in 
Fig.  364.  Each  of  these  dark  lines  indicates  that  a  par- 
ticular kind  of  ray  is  wanting  in  solar  light. 

AaBCD  EftP  G  HH' 


BOY  G  B  I  V 

FIG.  364. 

(a.)  The  spectra  of  incandescent  solids  are  continuous,  from  the 
extreme  red  to  a  limit  depending  upon  the  temperature.  The 
spectra  of  incandescent  gases  (not  containing  solid  particles  in 
suspension)  are  non -continuous,  consisting  of  a  number  of  definite 
bright  lines.  A  candle  or  gas  flame  gives  a  continuous  spectrum 
because  it  is  chiefly  due  to  the  incandescence  of  solid  carbon 
particles. 

(6.)  The  spectroscope  is  an  instrument  for  producing  and  observing 
pure  spectra.  It  has  proved  to  be  one  of  the  most  powerful  aids 
to  modern  science.  It  affords  the  most  delicate  means  of  chemical 
analysis ;  by  its  aid  several  elements  have  been  discovered ;  the 
presence  of  ^j^^^-y  of  a  grain  of  sodium  has  been  detected  by 
"  spectrum  analysis."  It  is  of  incalculable  importance  to  the 
astronomer.  For  definite  information,  the  pupil  is  necessarily 
referred  to  some  of  the  excellent  manuals  upon  the  subject  recently 
published. 

Experiment  I.— Let  the  rays  that  have  been  dispersed  by  a 
prism  fall  upon  a  convex  lens  as  shown  in  Fig.  365.  They  mil  be 
refracted  to  a  focus  and  recombined  to  form  white  light.  A  concave 
mirror  may  be  used  to  reflect  the  rays  to  a  focus  instead  of  using 
the  lens  as  above  described. 


CHROMATICS. 


FIG.  365. 

Experiment  2. — Make  a  "Newton's  disc"  of  cardboard  painted 
with  the  prismatic  colors  in  proper  proportion  as  indicated  by  Fig. 
366.  It  is  better  to  divide  the  surface  given  to  each  color  into 
smaller  sectors  arranged  alternately  as  shown  in  Fig.  367.  You 


FIG.  366. 


FIG.  367. 


may  paste  sectors  of  properly  colored  paper  upon  the  cardboard 
instead  of  painting  them.  Cause  this  disc  to  revolve  rapidly  by 
means  of  the  whirling  table  or  by  fastening  it  to  a  large  top.  Notice 
that  the  colors  are  blended  and  that  the  disc  appears  grayish  white. 

Experiment  3. — Hold  a  second  prism  near  one  that  is  used  to 
produce  a  solar  spectrum,  the  position  of  the  second  being  inverted 
with  reference  to  the  first.  If  the  dispersing  prism  be  held  as  shown 
in  Fig.  365,  the  second  should  be  held  with  the  refracting  edge 
uppermost,  the  facing  surfaces  being  parallel.  The  dispersed  rays 
emerging  from  the  first  prism  will  pass  through  the  second.  The 
rays  separated  by  the  first  will  be  again  blended  by  the  second  and 
appear  an  while  light. 

Experiment  4. — Hold  a  hand  mirror  near  the  dispersing  prism 
so  as  to  reflect  the  refracted  rays  to  a  distant  wall  or  ceiling.  Give 


520  CHROMATICS. 

to  the  mirror  a  rapid,  angular  motion  so  that  the  spectrum  is  made 
to  move  to  and  fro  very  quickly  in  the  direction  of  its  length. 
The  spectrum  changes  to  a  band  of  white  light  with  a  colored  spot  at 
each  end.  The  effect  is  due  to  what  is  known  as  the  "Persistence 
of  Vision,"  familiarly  illustrated  by  the  experiment  of  producing 
a  ring  of  light  by  whirling  a  firebrand  around  a  circle. 

704.  The  Composition  of  White  Light.— We 

have  now  shown,  by  both  the  processes  of  analysis  and 
synthesis,  that  white  light  is  composed  of  the  seven 
prismatic  colors.  We  have  decomposed  white  light 
into  its  seven  constituents  and  recombined  these  constit- 
uents into  white  light. 

Experiment  5. — Paint  three  narrow  strips  of  cardboard,  one 
vermilion  red,  one  emerald  green  and  the  other  aniline  violet. 
Be  sure  that  the  coats  are  thick  enough  thoroughly  to  hide  the 
cardboard.  When  dry,  hold  the  red  strip  in  the  red  of  the  solar 
spectrum  ;  it  appears  red.  Move  it  slowly  through  the  orange  and 
yellow  ;  it  grows  gradually  darker.  In  the  green  and  colors  beyond, 
it  appears  black.  Repeat  the  experiment  with  the  other  two  strips 
and  carefully  notice  the  effects. 

Experiment  6. — Make  a  loosely  wound  ball  of  candle  wick  ; 
soak  it  in  a  strong  solution  of  common  salt  in  water  ;  squeeze  most 
of  the  brine  out  of  the  ball ;  place  the  ball  in  a  plate  and  pour  al- 
cohol over  it.  Take  it  into  a  dark  room  and  ignite  it.  Examine 
objects  of  different  colors,  as  strips  of  ribbon  or  cloth,  by  this  yellow 
light.  Only  yellow  objects  will  have  their  usual  appearance. 

Experiment  7. — In  a  clear  tumbler  or  large  beaker  glass  of 
water,  dissolve  a  little  soap  (white  castile  is  desirable)  or  stir  a  few 
drops  of  an  alcoholic  solution  of  mastic.  Hold  the  vessel  in  the 
hand  and  examine  the  liquid  by  transmitted  sunlight.  Notice  that 
it  appears  yellowish-red.  In  a  small  test  tube,  either  liquid  will 
appear  colorless.  Place  a  black  screen  behind  the  vessel  and 
examine  the  liquid  by  reflected  sunlight.  Notice  that  it  appears 
blue. 

705.  Color  of  Bodies. — The  color  of  a  body  is  its 
property  of  reflecting  or  transmitting  to  the  eye  light  of 


THE   RAINBOW.  521 

that  particular  color,  the  other  rays  being  absorbed.    This 
power  may  be  described  as  selective  absorption. 

(a.)  Properly  speaking,  color  is  not  a  property  of  matter,  but  of 
light.  A  ribbon  is  called  red,  but  the  redness  belongs  to  the  light, 
not  to  the  ribbon.  There  would  be  more  propriety  in  saying  that 
the  ribbon  has  all  the  other  colors  of  the  rainbow,  because  it  absorbs 
the  others  and  reflects  the  red.  If  the  red  ribbon  be  placed  in  the 
green  or  blue  of  the  spectrum  it  will  appear  black  because  it 
receives  no  red  rays  to  reflect.  Colored  substances  decompose  the 
incident  light,  absorbing  some  rays  and  assuming  the  hue  of  those 
they  reflect  or  transmit  to  the  eye.  A  body  that  absorbs  very  few 
of  the  rays  is  white  ;  one  that  absorbs  nearly  all  is  black.  There- 
fore, black  is  not  a  color  but  its  absence. 

(6.)  If  the  rays  that  form  the  spectrum  be  divided  into  any  two 
parts  and  the  rays  in  each  part  be  mixed,  it  is  evident  that  each 
resultant  color  will  contain  what  the  other  needs  to  make  white 
light.  Such  are  called  complementary  colors  ;  either  is  said  to  be 
complementary  to  the  other.  The  mixture  of  colors  is  a  very 
different  thing  from  the  mixture  of  pigments. 

(c.)  Some  bodies  transmit  one  kind  of  rays  and  reflect  another. 
Thus,  gold  leaf  reflects  yellow  rays  and  transmits  green  rays.  The 
beautiful  blue  of  the  summer  sky,  the  terrible  black  of  the  storm 
cloud  and  the  matchless  sunset  hues  are  effects  due  to  the  reflec- 
tion, absorption  and  transmission  of  sunlight  by  particles  suspended 
in  the  atmosphere.  An  observer  placed  at  a  very  high  elevation, 
above  most  of  the  reflecting  particles  and  looking  into  outer  space, 
sees  no  blue  canopy  but  only  an  inky  darkness,  illumined  here  and 
there  by  some  gleaming  planet  or  twinkling  star. 

7O6.  The  Rainbow. — The  rainbow  is  due  to  re- 
fraction, reflection  and  dispersion  of  sunlight  by  water- 
drops.  The  necessary  conditions  are  : 

(1.)  A  shower  during  sunshine. 

(2.)  That  the  observer  shall  stand  with  his  back  to  the 
sun,  between  the  falling  drops  and  the  sun. 

(a.)  The  centre  of  the  circle  of  which  the  rainbow  forms  a  part 
is  in  the  prolongation  of  a  line  drawn  from  the  sun  through  thu 
eye  of  the  observer.  This  line  is  called  the  axis  of  the  bow. 


523  THE  RAINBOW. 

7O7.  Dispersion  by  a  Raindrop.— Suppose  the 

circle  whose  centre  is  at  0  (Fig.  368)  to  represent  the  section 


FIG.  368. 

of  a  raindrop.  A  ray  of  sunlight,  as  Sm,  falling  upon  the 
raindrop  would  be  refracted  at  m,  reflected  at  n,  and  again 
refracted  at  m'.  In  passing  thus  through  the  drop,  the 
light  is  also  decomposed.  If  m'E  represent  the  path  of 
a  red  ray,  the  violet  ray  will  traverse  a  path  above,  because 
violet  is  refracted  more  than  red.  The  path  of  this  violet 
ray  may  be  represented  by  m'B.  If  the  raindrop  be  in  the 
exact  position  for  the  red  ray,  m'E,  to  enter  the  eye  of  the 
observer,  the  violet  and  other  colored  rays  will  pass  over- 
head and  not  be  seen.  This  drop  will  appear  red. 

7O8.  Successive  Colors  of  the  Rainbow.— In  order 
that  a  violet  ray  may  enter  the  eye  at  E,  it  must  proceed  from  a  drop 
situated  below  the  one  that  sends  the  red  ray.  This  drop  will  appear 
violet.  Intervening  drops  will  give  the  intervening  colors  of  the 
solar  spectrum  in  their  proper  order  as  is  shown  in  Fig.  369.  Owing 
to  the  distance  of  the  sun,  all  of  the  incident  rays  are  parallel  with 
the  axis,  EO,  drawn  from  the  sun  through  E,  the  eye  of  the  ob- 
server, to  0,  the  centre  of  the  circle  of  which  the  bow  forms  a  part. 
The  angle  between  the  incident  and  the  emergent  ray,  SHE,  and 


THE  KAINBO 


OW. 


523 


consequently  the  angle,  REO,  is,  for  the  red  ray,  about  43°.     The 
angles  8'  F^and  VEO  are,  for  the  violet  ray,  about  40°.     The  other 


FIG.  369. 

colors  lying  between  these,  it  will  be  seen  that  the  angular  width  of 
the  rainbow  is  about  two  degrees. 

7O9.  Form  and  Extent  of  the  Rainbow. — 

From  Fig.  370,  it  will  be  seen  that  every  drop  in  the  arc  of 
a  circumference  drawn,  with  0  as 
a  centre  and  with  0  V  as  radius, 
being  opposite  the  sun  and  hav- 
ing the  same  angular  distance 
from  OE,  viz.,  40°,  will  send 
violet  colored  rays  to  the  eye  at  E, 
and  the  violet  colored  part  of 
the  bow  will  be  a  circular  arch.  FlG-  3?o- 

For  the  same  reason,  the  red  of  the  bow  is  a  circular  arch 
lying  without  the  violet  and  at  an  angular  distance  of  two 
degrees  therefrom  ;  the  other  colors  will  form  circular 


524:  THE  RAINBOW. 

arches  lying  between  these  two.  If  the  sun  he  at  the 
horizon,  EO  will  be  horizontal  and  the  arches  will  be 
semicircles.  If  the  sun  be  above  the  horizon,  0  will  be  de- 
pressed below  the  horizon  and  less  than  semicircles  will  be 
seen.  If  the  observer  be  on  a  mountain-top  or  up  in  u 
balloon,  he  may  see  more  than  a  semicircle. 

71O.  The  Secondary  Bow. — Sometimes  two  col- 
ored arches  are  seen,  one  within  the  other.  The  inner 
which  we  have  just  considered  is  called  the  primary  bow ; 
the  outer,  the  secondary  bow. 

(a.)  In  explaining  the  primary  bow,  we  traced  a  ray  of  light  fall- 
ing upon  the  top  of  the  raindrop ;  to  explain  the  secondary  bow,  wo 
trace  a  ray  falling  upon  its  lower  part.  Such  a  ray,  as  Sm,  will  be 
refracted  at  m,  reflected  at  n  and  n' ' ,  and  again  refracted  at  m', 
coming  to  the  eye  at  E.  If  the  ray  which  thus  comes  to  the  eye  at 
E  be  a  red  ray,  the  violet  will  follow  m1  F,  and  thus,  passing  below 
the  eye  because  of  its  greater  refrangibility,  be  lost  to  sight.  The 
drop  that  sends  a  violet  ray  to  the  eye  at  7£must  be  placed  above 
instead  of  below  the  drop  that  sends  the  red  ray.  (Fig.  371.) 


FIG.  371. 

(6.)  In  the  secondary  bow,  the  red  arch  will  be  on  the  inside,  with 
an  angular  distance  from  the  axis,  EO,  of  about  51°,  while  the  violet 


CHROMATICS— SPECTRA.  525 

will  be  on  the  outside  at  an  angular  distance  of  about  54°.  In  the 
case  of  either  bow,  some  light  is  lost  at  each  reflection  ;  therefore, 
since  there  are  more  reflections  in  the  secondary  bow,  this  will 
appear  fainter. 

711.   Chromatic  Aberration. — It  is  impossible, 
by  means  of  a  single  spherical  convex  lens,  to  bring  all  of 
the  incident  rays  to  a  common  focus.    The  blue  and  violet 
rays   being  refracted  more  than 
the   red   rays   will    converge    at 
points  nearer  the  lens.     In  con- 
sequence of  this,  when  an  image 
is  projected  upon  a  screen,  the 
image  is  surrounded  with  a  col- 
ored border,  the  color  depending  upon  the  distance  of  the 
screen  from  the  lens.     This  inability  of  a  single  lens 
to  bring  differently  colored  rays  to  the  same  focus 
is  called  chromatic  aberration. 


Achromatic  Lens.— A  convex  lens  of  crown 
glass,  by  combination  with  a  concave  lens  of  flint  glass,  may 
have  its  dispersive  power  neutralized  without  completely 
neutralizing  its  refraction.  As  the  converging  effect  of  the 
compound  lens  is  not  destroyed,  images  may  be  formed ; 
as  the  dispersive  effect  is  destroyed,  the  colored  fringe  is 
avoided.  Jl  combination  of  lenses  by  which  disper- 
sion is  avoided  and  refraction  secured  is  called  an 
achromatic  lens. 

Experiment  8. — In  any  convenient  clamp,  firmly  press  together 
two  pieces  of  clean,  thick,  plate  glass.  A  beautiful  play  of  colors 
will  be  seen  in  the  glass. 

713.  Interference  of  Light.— If  a  plano-convex 
lens  of  very  small  curvature  be  pressed  down  upon  a  flat 
plate  of  glass  and  looked  at  from  above,  colored  rings 


526  Ctttt  OMA  TICS—  SPECT&A. 

(known  as  Newton's  rings)  may  be  seen  around  the  centre 
of  the  lens.  If  the  light  be  homogeneous  (i.  e.}  composed 
of  one  kind  of  rays,  as  red)  instead  of  white,  the  rings  will 
be  separated  by  dark  spaces.  The  dark  rings  are  due  to 
the  interference  of  the  ether  waves  reflected  from  the 
lower  surface  of  the  lens  and  from  the  upper  surface  of  the 
plate  respectively.  Whenever  the  distance  between  the 
two  reflecting  surfaces  is  such  that  the  two  sets  of  waves 
unite  in  opposite  phases,  a  dark  ring  will  appear.  Two 
luminous  waves,  as  well  as  two  sound  waves  (§  515),  may 
unite  so  as  to  destroy  each  other.  When  white  light  is 
used,  the  color  in  any  given  ring  is  complementary  to  the 
color  that  is  destroyed  by  interference.  Similar  colors  are 
often  seen  in  soap  bubbles,  in  small  quantities  of  oil  that 
have  been  spread  over  large  sheets  of  water,  in  mica,  seli- 
nite  and  other  crystals  that  easily  cleave  into  thin  plates, 
etc.,  and  are  due  to  the  interference  of  light  reflected  from 
two  surfaces  very  near  each  other. 

Experiment  9. — Cover  one  side  of  a  pane  of  glass  with  India  ink, 
being  sure  that  it  is  made  opaque.  Scratch  20  parallel  lines  about 
2  mm.  apart,  upon  the  glass,  so  that  the  light  may  pass  through. 
Standing  about  6  or  7  meters  from  a  lamp,  with  one  eye  shut  and 
the  other  shaded  from  the  sunlight,  look  through  the  lines  ruled  on 
the  glass  at  the  flame.  Slowly  moving  the  glass  toward  and  from 
the  eye,  such  a  position  may  be  found  for  it  that  many  spectra  of 
the  flame  may  be  seen  separated  by  dark  spaces. 

Experiment  10. — Throw  a  sunbeam  through  a  very  small  open- 
ing in  the  shutter  of  a  darkened  room.  Receive  the  beam  upon  a 


FIG.  373. 

convex  lens  of  short  focal  length,  placing  a  piece  of  red  glass  be- 
tween the  aperture  and  the  lens.     Place  an  opaque  screen  with  a 


CHROMATICS— SPECTRA.  52? 

sharp  edge  beyond  the  focal  distance  of  the  lens,  as  at  e,  so  as  to 
cut  off  the  lower  part  of  the  luminous  cone  and  project  the  upper 
part  thereof  upon  a  screen  at  b.  A  faint  light  is  seen  on  the  screen 
below  the  level  of  b  and,  therefore,  within  the  geometrical  shadow. 
Jhe  part  of  the  screen  immediately  above  the  level  of  b  contains  a 
series  of  dark  and  light  bands  as  shown  at  B,  which  is  a  front  view 
of  the  screen  at  b. 

714.  Diffraction. — The  pupil  may  have  noticed  that 
when  water  waves  strike  a  rock  or  other  obstacle  a  little 
ways  from  the  shore,  part  of  the  energy  of  the  wave  is 
expended  in  producing  a  second  set  of  waves  that  seem  to 
circle  outward  from  the  side  of  the  obstacle  as  a  centre. 
The  original  wave,  which  we  may  call  the  primary,  passes 
directly  onward  while  the  other  waves,  which  we  may  call 
secondary,  wind  around  behind  the  obstacle.  In  similar 
manner,  luminous  waves  are  modified  when  they  pass  the 
edge  of  an  opaque  body,  as  in  going  through  a  narrow 
slit,  in  consequence  of  which  the  rays  seem  to  be  bent 
and  to  penetrate  into  the  shadow.  Such  an  apparent 
bending  of  the  luminous  rays  is  called  diffraction. 
As  the  primary  and  secondary  waves  cut  each  other,  they 
will  unite  at  some  points,  crest  with  crest  and,  at  other 
points,  crest  with  trough.  At  the  latter  points,  we  shall 
have  interference  of  light  and  the  effects  of  colors  pro- 
duced thereby  as  explained  above.  The  halos  sometimes 
seen  around  the  sun  and  moon  are  due  to  the  diffraction 
of  light  by  watery  globules  in  the  atmosphere.  The  colors 
often  seen  on  looking  through  a  feather  or  one's  half- 
closed  eyelashes  at  a  distant  source  of  brilliant  light  are 
also  due  to  diffraction. 

Experiment  II. — Look  carefully  at  the  black  and  the  white  circles 
given  in  Fig.  374  and  determine  which  seems  to  be  the  larger. 
Then  carefully  measure  their  diameters  and  see  which  is  the  larger. 


528  CHROMATICS— SPECTRA. 

715.  Irradiation.—.^  white  or  very  bright  object 
seen  against  a  black  ground  appears  larger  than  it 


FIG.  374. 

really  is ;  a  black  object  on  a  ivhite  ground  appears 
smaller  than  it  really  is.  This  effect  is  called  irra- 
diation. It  arises  from  the  fact  that  the  impression 
produced  by  a  bright  object  on  the  retina  extends  beyond 
the  outline  of  the  image. 

(a.)  The  effect  of  irradiation  is  very  perceptible  in  the  apparent 
magnitude  of  stars  which  are  thus  made  to  appear  much  larger  than 
they  otherwise  would  ;  also  in  the  appearence  of  the  new  moon,  the 
illuminated  crescent  seeming  to  extend  beyond  the  darker  portion, 
the  new,  thus,  holding  the  old  moon  in  its  arms. 

716.  Properties  of  the  Sunbeam. — We  have  seen  that 
we  may  decompose  a  sunbeam  by  availing  ourselves  of  the  varying 
refrangibility  of  the  different  kinds  of  rays  of  which  it  is  composed. 
We  have  been  able  in  this  manner  to  produce  the  seven  prismatic 
colors  from  white  light.     But  our  analytic  investigations  must  go 
still  further.     Beyond  the  limits  of  the  visible  spectrum,  in  both 
directions,  there  are  rays  that  do  not  excite  the  optic  nerve,  the  ex- 
istence of  which,  however,  may  be  easily  proved.     The  sunbeam 
has  three  properties  which  we  must  consider  in  detail :  luminous, 
thermal  and  actinic. 

717.  Luminous  Kays. — The  difference  in  color  be- 
tween the  rays  found  in  different  parts  of  the  spectrum  is 
merely  one  of  rate  of  vibration  or  wave-length.     In  respect 


CHROMATICS— SPECTRA.  529 

to  the  visible  spectrum,  it  may  be  said  that  color  is  to 
light  what  pitch  is  to  sound.  The  length  of  an  ether- 
wave  that  can  awaken  the  sensation  of  redness  is  about 
Tsoiro  °f  an  incn;  °f  one  ^nat  can  awaken  the  sensation  of 
violet,  about  -^\-Q-Q.  The  waves  corresponding  to  the 
intermediate  colors  have  intermediate  lengths.  The 
visibility  or  invisibility  of  certain  rays  depends  on  the 
construction  of  the  eye  rather  than  on  any  peculiarity  of 
the  rays.  It  is  quite  possible  that  the  eyes  of  some 
animals  are  so  constructed  that  ultra-red  rays  may  excite 
vision,  and  that  the  eyes  of  other  animals  are  so  con- 
structed that  ultra-violet  rays  may  excite  vision. 

718.  Thermal  Rays. — If    a  very    delicate    ther- 
mometer or  thermopile  be  successively  placed  in  various 
parts  of  the  spectrum  it  will  be  found  that  the  tempera- 
ture is  scarcely  affected  in  the  violet,  but  that  there  is  a 
continual  increase  in  temperature  as  the  thermometer  is 
moved  toward  the  other  end  of  the  spectrum,  it  being 
quite  marked  in  the  red  and  even  beyond  the  red,  wholly 
outside  the  visible  spectrum.     We  thus  detect  ultra-red 
rays  constituting  a  heat  spectrum.     Their  position 
indicates  their  low    refrangibility  and    increased    wave- 
length.    Because  of  its  diathermancy,  a  rock-salt  prism  is 
desirable  for  this  experiment ;  glass  absorbs  most  of  the 
ultra-red  rays. 

(«.)  The  oxy-hydrogen  flame  (Chemistry,  §  41)  develops  little 
light  but  an  intense  heat.  Most  of  its  rays  are  obscure  heat  rays. 
If  a  small  cylinder  of  lime  be  held  in  this  flame,  it  emits  a  most 
brilliant  light.  This  change  of  obscure  heat  rays  into  luminous  rays 
is  called  color escence. 

719.  Actinic  Rays. — The  actinic  or  chemical  effects 


530  CHROMATtOS—  SPECTRA. 

of  sunlight  are,  in  a  general  way,  familiar  to  all.  For 
example,  plants  absorb  carbon  from  the  atmosphere  only 
during  the  day  time.  Silver  chloride  is  very  sensitive  to 
this  action  of  sunlight.  The  sensitive  paper  of  the  photog- 
rapher will  remain  unchanged  in  the  dark  ;  it  will  be 
quickly  blackened  in  the  light.  If  a  piece  of  paper  freshly 
washed  in  a  solution  of  sulphate  of  quinine,  or  some  other 
fluorescent  substance,  be  held  in  the  ultra-violet  rays,  it 
will  become  visible.  Such  a  slip  of  paper  may  be  used  as 
a  test  for  the  presence  of  actinic  rays.  By  placing  it 
successively  in  the  different  parts  of  the  visible  spectrum, 
it  will  be  affected  least  in  the  red  and  most  in  the  violet. 
Actinic  effects  will  be  found  even  beyond  the  violet,  wholly 
outside  the  visible  spectrum. >  We  thus  detect  ultra- 
violet rays  constituting  an  actinic  spectrum.  Their 
position  indicates  their  high  ref rangibility ;  that  their 
wave-length  is  less  than  that  of  the  violet  rays.  A  quartz 
prism  is  desirable  for  this  experiment  as  glass  quenches 
most  of  the  actinic  rays.  The  change  of  obscure,  actinic 
rays  into  luminous  rays  is  called. fluorescence.  -jL 

72O.  The  Electric  Light.— The  electric  light  is 
particularly  rich  in  these  invisible  rays.  The  dark  heat 
rays  may  be  sifted  from  the  beam  of  light  by  passing  it 
through  a  transparent  solution  of  alum;  only  the  lumi- 
nous rays  will  be  allowed  to  pass.  The  luminous  rays  may 
be  sifted  out  by  sending  the  beam  through  an  opaque  solu- 
tion of  iodine  in  carbon  di-sulphide.  If  these  solutions 
be  placed  in  spherical  flasks,  they  will  constitute  lenses 
that  will  refract  the  transmitted  rays  to  well-defined  foci. 
The  focus  of  the  transparent  solution  will  be  brilliantly 
illuminated,  but  will  have  little  heating  power;  that  of 


CHROMATICS— SPECTRA.  531 

the  opaque  solution  will  be  invisible,  while  gun-cotton 
placed  there  may  be  instantly  exploded.  Platinum-foil 
has  been  raised  to  a  red  heat  at  one  of  these  dark  foci. 
Photographs  are  now  frequently  taken  by  the  electric  light. 

721.  Selective  Radiation  and  Absorption.— 

Radiation  of  light  or  heat  consists  in  giving  motion  to 
the  ether;  absorption  consists  in  taking  motion  from  the 
ether.  Molecules  of  one  kind  are  able  to  vibrate  at  one 
rate  ;  those  of  another  kind  may  be  obliged  to  vibrate  at 
a  different  rate.  The  first  set  of  molecules  may  be  able  to 
give  to  the  ether,  or  take  from  it,  a  rate  of  vibration  which, 
in  the  ether,  constitutes  obscure  heat.  These  molecules 
can  absorb  or  radiate  obscure  heat.  They  may  be  unable 
to  vibrate  at  the  higher  rate  which  will  enable  them  to  ab- 
sorb or  radiate  light.  They  must  either  transmit  or  reflect 
light  that  falls  upon  them.  In  other  words,  a  body  absorbs 
with  special  energy  the  kind  of  rays  itself  can  radiate, 
both  the  absorption  and  the  radiation  depending  upon  the 
possible  rate  of  vibration  of  the  molecules  of  the  body. 

(a.)  In  the  case  of  gases,  the  period  of  molecular  vibration  is 
sharply  defined.  Gaseous  molecules,  like  musical  strings,  can 
vibrate  at  only  definite  rates.  Liquid  and  solid  molecules,  like 
sounding-boards,  are  able  to  vibrate  at  different  rates  lying  between 
certain  fixed  limits.  These  limits  depend  largely  upon  the  tempera- 
ture. This  principle  underlies  solar,  spectrum  analysis. 

722.  Relation  between  Radiation  and  Ab- 
sorption.— Transparent  bodies  are  transparent  because 
the  ether-waves  which  produce  or  constitute  light  pass  be- 
tween the  molecules  of  such  bodies  without  having  their 
wave-motion  transferred  to  the  molecules.    Diathermanous 
bodies  transmit  heat  freely  because  the  ether-waves  which 
produce  or  constitute  heat  pass  between  the  molecules  of 


532 


CHR  OMA  TICS— SPECTRA. 


such  bodies  without  having  their  peculiar  wave-motion 
transferred  to  the  molecules  of  the  body  through  which 
they  pass.  When  a  ray  of  light  or  heat,  in  passing  through 
a  substance,  gives  its  energy  to  the  molecules  between 
which  it  is  passing  in  the  ether,,  the  ray  is  absorbed.  It 
no  longer  exists  as  radiant  energy;  it  has  become  absorbed 
heat  and  warms  the  body.  It  is  no  longer  a  motion  of 
the  ether;  it  has  become  a  motion  of  ordinary  matter. 
As  in  the  case  of  radiant  heat,  so  with  light;  the  best 
absorbents  are  the  best  radiators.  A  piece  of  transparent, 
colorless  glass  will  absorb  very  little 
fight ;  heat  it  intensely  and  it  will 
radiate  very  little  light.  On  the 
other  hand,  a  piece  of  opaque  glass 
will  absorb  a  great  deal  of  light ; 
when  heated  intensely,  it  will  radi- 
ate a  great  deal  of  light.  See  §625. 

(«.)  If  an  intensely  heated  pot  of  melted  FlG-  375- 

lead,  tin  or  plumber's  solder  be  carried  into  a  dark  place  and  the  dross 

skimmed  aside  by  a  red-hot 
iron  ladle,  the  liquid  metal 
(which  in  sunlight  would 
reflect  rather  than  absorb 
the  light)  will  appear  less 
bright  than  the  surround- 
ing dross.  If  a  piece  of 
platinum-foil  bearing  an 
ink-mark  be  heated  to  in- 
candescence and  viewed  in 
a  dark  room,  the  ink-mark 
will  radiate  more  light 
than  the  metal.  Exposed 
to  sunlight,  the  ink-mark 
will  absorb  more  light  than 
the  metal.  If  a  chalk-mark 
be  made  on  a  black  poker, 
FIG.  376.  the  poker  heated  red-hot 


EXERCISES. 


533 


and  viewed  in  a  dark  room,  the  chalk  will  be  less  luminous  than  the 
iron.  If  a  piece  of  stone-  ware  of  black  and  white  pattern  (Fig.  375? 
be  heated  to  redness  and  viewed  in  a  dark  room,  the  black  will  shine 
more  brightly  than  the  white,  the  pattern  being  reversed  as  shown 
in  Fig.  376. 

EXEKCISES. 

1.  Give  the  best  reason  you  can  think  of,  why  the  rainbow  is  a 
circular  arc  and  not  a  straight  line  or  of  some  other  shape. 

2.  Taking  the  velocity  of  light  to  be  188,000  miles  per  second  and 
the  wave-length  for  green  light  to  be  .00002  of  an  inch,  how  many 
waves  per  second  beat  upon  the  retina  of  an  eye  exposed  to  green 
light? 

3.  How  may  spherical  and  chromatic  aberration  caused  by  a  lens 
be  corrected  ? 

4.  Describe  Fraunhofer's  lines  and  tell  how  they  may  be  produced. 
Why  not  through  a  circular  orifice  ? 

5.  Describe  in  full  what  is  meant  by  dispersion  and  the  dispersive 
power  of  a  medium. 

Recapitulation.  —  To  be  amplified  by  the  pupil  for 
review. 


r  DISPERSION. 


COMPLEXITY  OF 
SUNBEAM.. 


CO 

u 


ANALYSIS.. 


By  Prisms. 


*•  SPECTRA.  . 


SYNTHESIS.  -I 


By  Water  Drops. 

Solar. 

Luminous. 

Thermal. 
I  Actinic. 
BY  LENSES. 
BY  MIRRORS. 
BY  PRISMS. 
BY  PERSISTENCE  OF  VISION, 


U 


(CAUSE   OF. 
COMPLEMENTARY. 
SKY. 

INTERFERENCE. 

DIFFRACTION. 

IRRADIATION. 

RADIATION  AND  ABSORPTION  RELATED, 


534  OPTICAL  INSTRUMENTS. 


ECTFON   V. 


OPTICAL  INSTRUMENTS.— POLARIZATION. 

723.  Photographers'  Camera.— The  photogra^ 
pher's  camera  is  nearly  the  same  as  the  camera-obscura 
described  in  §  650.    Instead  of  the  darkened  room  we  have 
a  darkened  box,  DE;  instead  of  the  simple  hole  in  the 
shutter,  we  have  an  achromatic  convex  lens,  placed  in  a 
sliding  tube  at  A. 

(a.)  Sometimes,  one  part  of  the  box  slides  within  the  other  part 
with  a  movement  like  that  of  a  telescope  tube.  Sometimes  the  front 
and  the  back  of  the  box  are  joined  by  flexible  sides,  as  shown  in 
Fig.  377,  so  that  the  distance  between  A  and  E  may  be  varied.  A 
ground -glass  plate  is  placed  in  the  frame  at  E,  which  is  adjusted  so 

that  a  well-defined,  inverted 
image  of  the  object  in  front 
of  A  is  projected  upon  the 
glass  plate.  (See  §694.)  This 
adjustment,  or  "focussing," 
is  completed  by  moving  the 
lens  and  its  tube  by  the 
toothed  wheel  at  D.  When 
the  "  focussing "  is  satis- 
factory, A  is  covered  with 
a  black  cloth,  the  ground- 

glass  plate  rePlaced  b^  a 
chemically- prepared  sensi- 
tive plate,  the  cloth  removed  and  the  image  projected  thereon.  The 
light  works  certain  chemical  changes  where  it  falls  upon  this  plate 
and  thus  a  more  lasting  image  is  produced.  The  preliminary  and 
subsequent  processes  necessarily  involved  in  photography  cannot  be 
considered  here ;  they  belong  rather  to  chemistry. 

724.  The  Human  Eye.— This  most  admirable  of 
all  optical  instruments  is  a  nearly  spherical  ball,  capable  of 


OPTICAL  INSTRUMENTS.  535 

being  turned  considerably  in  its  socket.  The  outer  coat,  S, 
is  firm  and,  excepting  in  front,  is  opaque.  It  is  called 
the  "white  of  the  eye,"  or  the  sclerotic  coat.  Its  trans- 
parent part  in  front,  (7,  is  called  the  cornea.  The  cornea 
is  more  convex  than  the 
rest  of  the  eyeball.  The 
cornea  fits  into  the  coat,  S, 
as  a  watch  crystal  does  into 
its  case.  Behind  the  cornea, 
is  a  curtain,  /,  called  the 
iris.  It  is  colored  and 
opaque;  the  circular  window 
in  its  centre  is  called  the 
pupil.  The  color  of  the  FlG-  378. 

iris  constitutes  the  color  of  the  eye.  Back  of  the  pnpil  is 
the  crystalline  lens,  L,  built  of  concentric  shells  of  varying 
density.  Its  shape  is  shown  in  the  figure.  This  lens 
divides  the  eye  into  two  chambers,  the  anterior  chamber 
containing  a  limpid  liquid  called  the  aqueous  humor  ;  the 
posterior  chamber  containing  a  transparent  jelly,  V,  called 
the  vitreous  humor.  The  viteous  humor  is  enclosed  in  a 
transparent  sack,  H,  called  the  hyaloid  membrane.  The 
cornea,  aqueous  humor,  crystalline  lens  and  vitreous 
humor  are  refracting  media.  Back  of  the  hyaloid  mem- 
brane is  the  retina,  R,  an  expansion  of  the  optic  nerve. 
At  the  centre  of  the  back  of  the  eye  is  a  slight  depression 
called  the  yellow  spot.  This  is  the  most  sensitive  part  of 
the  retina.  The  point  at  which  the  optic  nerve  enters  the 
eye  is  called  the  blind  spot.  It  is  at  one  side  of  the  yellow 
spot,  nearer  the  nose.  Between  the  retina  and  the 
sclerotic  coat  is  JV?  the  choroid  coat,  intensely  black  and 
opaque, 


536  OPTICAL  INSTRUMENTS. 

The  eye,  optically  considered,  is  simply  an  arrangement 
for  projecting  inverted  real  images  of  visible  objects  upon 
a  screen  made  of  nerve  filaments.  The  image  thus 
formed  is  the  origin  of  the  sensation  of  vision.  (§  650  c.) 

Experiment  P.— Stick  two  needles  into  a  book-cover  or  board 
about  6  inches  apart.  Close  one  eye  and  hold  the  book  so  that  the 
needles  shall  be  nearly  in  range  with  the  open  eye  and  about  6  and  12 
inches  respectively  from  it.  One  needle  will  be  seen  distinctly 
while  the  image  of  the  other  will  be  blurred.  Fix  the  view 
definitely  on  the  needle  that  appears  blurred  and  it  will  become 
distinct,  but  you  cannot  see  both  clearly  at  the  same  time.  (See  Fig. 
354.) 

Experiment  2.— Close  the  left  eye,  look  steadily  at  the  cross  be- 
low, holding  the  book  about  a  foot  from  the  face.  The  dot  is 


plainly  visible  as  well  as  the  cross.  Keep  the  eye  fixed  on  the  cross 
and  move  the  book  slowly  towards  the  face.  When  the  image  of 
the  dot  falls  on  the  blind  spot  of  the  eye,  the  dot  will  disappear. 
Hold  the  book  in  this  position  for  a  moment  and  see  if  the  changing 
convexity  of  the  crystalline  lens  throws  the  image  of  the  dot  off  the 
blind  spot,  making  the  dot  again  visible. 

Experiment  3. — Stick  a  bright  red  wafer  upon  a  piece  of  white 
paper.  Hold  the  paper  in  a  bright  light  and  look  steadily  at  the 
wafer,  for  some  time,  with  one  eye.  Turn  the  eye  quickly  to 
another  part  of  the  paper  or  to  a  white  wall  and  a  greenish  spot, 
the  size  and  shape  of  the  wafer,  will  appear.  The  greenish  color 
of  the  image  is  complementary  to  the  red  of  the  wafer.  If  the  wafer 
be  green,  the  image  afterward  seen  will  be  of  a  reddish  (comple- 
mentary) color. 

725.  The  Action  of  the  Eye.— The  iris  acts  as  a 
self-regulating  diaphragm,  dilating  the  pupil  and  thus 
admitting  more  light  when  the  illumination  is  weak  ;  con- 
tracting the  pupil  and  cutting  off  more  light  when  the 
illumination  is  strong.  The  adjustment  for  distance 
(necessary  to  throw  the  foci  on  the  retina)  is  effected  by 


OPTICAL  INSTRUMENTS.  537 

changing  the  convexity  of  the  anterior  surface  of  the 
crystalline  lens.  (See  Experiment  2.)  The  impression 
upon  the  retina  does  not  disappear  instantly  when  the 
action  of  the  light  ceases  but  continues  for  about  an 
eighth  of  a  second.  The  result  is  what  is  called  the  per- 
sistence of  vision.  If  the  impressions  are  repeated  within 
the  interval  of  the  persistence  of  vision,  they  appear  con- 
tinuous. (Compare  §  490.)  This  phenomenon  is  well 
illustrated  by  the  luminous  ring  produced  by  swinging  a 
firebrand  around  a  circle  and  in  the  action  of  the  common 
toy  known  as  the  thaumatrope  or  the  zoetrope.  The 
sensibility  of  the  retina  is  easily  exhausted,  as  though  the 
terminal  cones  of  the  optic  nerve  became  tired  of  vibrat- 
ing at  a  given'rate  and  thus  became  insensible  to  certain 
impulses  of  light  corresponding  to  a  certain  color.  (See 
Experiment  3.)  The  retinas  of  some  eyes  seem  to  be 
affected  similarly  by  rays  of  different  colors.  The  owners 
of  such  eyes  are  said  to  be  color  blind.  Serious  railway 
accidents  caused  by  mistaking  the  color  of  signal  lights, 
have  led  to  examinations  for  color  blindness.  Such  ex- 
aminations have  shown  that  this  optical  defect  is  much 
more  common  than  is  generally  supposed,  many  persons 
being  color  blind  without  knowing  it. 


Estimates  of  Size  and  Distance.—  We 

estimate  the  size  of  visible  objects  (by  instinct  or  by  ex- 
perience) from  the  visual  angle  and  the  supposed  distance 
of  the  object  and  by  comparison  with  objects  of  known 
size.  If  we  are  mistaken  in  the  distance  of  the  object,  we 
are  often  mistaken  in  our  estimate  of  its  size.  We  estimate 
the  distance  of  an  object  by  the  distinctness  with  which 
we  see  it,  by  comparison  with  objects  of  known  distance 


538  OPTICAL  INSTRUMENTS. 

and  by  the  muscular  effort  we  make  in  turning  the  eyes 
inward  so  as  to  direct  them  upon  the  object.  The  axes  of 
the  eyes  intersect  at  the  object.  The  angle  between  the 
axes  is  called  the  optical  angle.  The  greater  the  optical 
angle,  the  less  the  distance. 

(a.)  The  more  obscure  an  object,  the  more  distant  (and,  conse- 
quently, the  larger)  it  seems  to  be.  Hence,  the  apparent  enormous 
size  of  objects  seen  in  a  fog.  When  the  moon  appears  on  the  hori- 
zon, we  see  that  she  is  beyond  all  terrestrial  objects  in  that  direction 
and  she  seems  farther  off  (and,  consequently,  larger)  than  when  she 
is  overhead,  there  being  then  no  intervening  objects  for  comparison. 
But  the  moon  is  actually  nearer  us  when  she  is  in  the  zenith  than 
when  in  the  horizon  and  the  visual  angle  is,  consequently,  greater. 

727.  Distinct  Vision. — That  vision  may  be 
distinct,  the  image  formed  on  the  retina  must  be 
clearly  defined,  well  illuminated  and  of  sufficient 
size. 

(a.)  The  power  of  the  eye  to  adjust  itself  for  distance  is  limited. 
When  a  book  is  held  close  to  the  eyes,  the  rays  from  the  letters  are 
50  divergent  that  the  eye  cannot  focus  them  upon  the  retina.  The 
jear  point  of  vision  is  generally  about  3^  inches  from  the  eye.  As 
parallel  rays  are  generally  brought  to  a  focus  on  the  retina  when  the 
eye  is  at  rest,  the  far  point  for  good  eyes  is  infinitely  distant.  Owing 
T,O  the  small  size  of  the  pupil,  rays  from  a  point  20  inches  or  more 
distant  are  practically  parallel. 

(&.)  The  near  point  of  some  eyes  is  less  than  3^  inches,  while  the 
far  point  is  only  8  or  10  inches.  The  owners  of  such  eyes  are  near- 
sighted.  In  such  eyes,  the  retina  is  too  far  back,  the  eyeball  being 
elongated  in  the  direction  of  its  axis.  The  remedy  is  in  concave 
glasses. 

(c.)  The  near  point  of  some  eyes  is  about  12  inches  and  the  far 
point  is  infinitely  distant.  The  owners  of  such  eyes  are  far-sighted. 
In  such  eyes  the  retina  is  too  far  forward,  the  eyeball  being  flat- 
tened in  the  direction  of  its  axis.  The  remedy  is  in  convex  glasses. 

(d.)  The  eye  loses  its  power  of  adjustment  with  age,  the  crystal- 
line lens  losing  its  elasticity.  The  cause  of  the  difficulty  is  different 
from  that  of  far  sightedness,  but  the  remedy  is  the  same. 


OPTICAL   INSTRUMENTS. 


539 


728.  Magnifying  Glasses.— A  magnifying  glass, 
or  simple  microscope,  is  a  convex  lens,  generally  double- 
convex.     The  object  is  placed  between  the  lens  and  its 
principal  focus.     The  image  is  virtual,  erect  and  magni- 
fied (Fig.  361.)     The  visual  angle  subtended  by  the  image 
is  greater  than  that  subtended  by  the  object. 

729.  Compound  Microscope. — The  compound 
microscope  consists  of  two  or 

more  convex  lenses  placed  in 
a  tube.  One  of  these,  o, 
called  the  object  glass  or  ob- 
jective, is  of  short  focus.  The 
object,  ab,  being  placed  slightly 
beyond  the  principal  focus,  a 
real  image,  cd,  magnified  and 
inverted,  is  formed  within  the 
tube  (§  695).  The  other  lens, 
E,  called  the  eyeglass,  is  so 
placed  that  the  image  formed 
by  the  objective  lies  between 
the  eyeglass  and  its  focus.  A 
magnified  virtual  image,  AB, 
of  the  real  image  is  formed 
by  the  eyeglass  (§  696)  and 
seen  by  the  observer.  (See 
Fig.  379.) 


FIG.  379. 


(a.)  Compound  microscopes  are  usually  provided  with  several 
objectives  of  different  focal  distances,  so  that  a  selection  may  be 
made  according  to  the  magnifying  power  required.  The  powers 
generally  used  range  from  50  to  350  diameters  (i.  e.,  they  multiply 
linear  dimensions  so  many  times).  The  object  generally  needs  to 
be  intensely  illuminated  by  a  concave  mirror  or  convex  lens. 


540 


OP  TIC  A  L   INSTR  UMENTS. 


73O.  Galilean  Telescope;   Opera  Glass.— In 
the  telescope  attributed  to  Galileo,  the  objective  is  a  double 


FIG.  380. 

convex  and  the  eye-piece  is  a  double  concave  lens.  The 
concave  lens  intercepts  the  rays  before  they  have  reached 
the  focus  of  the  objective  ;  were  it  not  for  this  eye-piece,  a 
real,  inverted  image  would  be  formed  back  of  the  position 
of  the  concave  lens.  The  rays  from  A,  converging  after 
refraction  by  0,  are  rendered  diverging  by  (7;  they  seem  to 
diverge  from  a.  In  like  manner,  the  image  of  B  is  formed 
at  b.  The  image,  ab,  is  erect  and  very  near.  An  opera- 
glass  consists  of  two  Galilean  telescopes  placed  side  by 
side.  In  a  good  instrument,  both  lenses  are  achromatic. 

731.  Astronomical  Telescope;  Refractor. — 

Astronomical  telescopes  are  of  two  kinds — refractors  and 


FIG.  381. 

reflectors.  Fig.  381  represents  the  arrangement  of  the 
lenses  and  the  direction  of  the  rays  in  the  refracting 
telescope.  The  object-glass  is  of  large  diameter  that  it 
may  collect  many  rays  for  the  better  illumination  of  the 
image.  The  inverted,  real  image  formed  by  the  objective, 


OPTICAL  INSTRUMENTS.  541 

0,  is  magnified  by  the  eye-piece,  as  in  the  case  of  the 
compound  microscope.  The  visible  image,  cd,  is  a  virtual 
image  of  ab,  the  real  image  of  AB. 

(a.)  The  telescope  now  building  for  the  Lick  Observatory  (on  the 
summit  of  Mt.  Hamilton,  California,  4,400  ft.  above  the  level  of  the 
sea)  will  be  the  largest  refractor  in  the  world.  The  objective  is  38j 
inches  in  diameter.  The  telescope  will  be  60  ft.  in  length.  The 
two  glasses  will  cost  $51,000  ;  the  mounting  will  cost  as  much  more  ; 
the  dome  of  the  Observatory  will  cost  $50,000. 

732.  Reflecting  Telescopes. — A  reflecting  tele- 
scope consists  of  a  tube  closed  at  one  end  by  a  concave 


FIG.  382. 

mirror,  so  placed  that  the  image  thus  formed  may  be  mag- 
nified by  a  convex  lens  used  as  an  eye-piece.  Sometimes 
the  eye-piece  consists  of  a  series  of  convex  lenses  placed 
in  a  horizontal  tube,  as  shown  in  Fig.  382.  The  rays 
from  the  mirror  may  be  reflected  by  a  cathetal  prism,  mn 
(§  686  [c]),  and  a  real  image  formed  at  ab.  This  image  is 
magnified  by  the  glasses  of  the  eye-piece  and  a  virtual 
image  formed  at  cd.  The  Earl  of  Rosse  built  a  telescope 
with  a  mirror  six  feet  in  diameter  and  having  a  focal  dis- 
tance of  fifty-four  feet.  (Appendix  T.) 

733.  Terrestrial  Telescope.— The  inversion  of 
the  image  in  an  astronomical  telescope  is  inconvenient 
when  viewing  terrestrial  objects.  This  inconvenience  is 


542 


OPTICAL   INSTRUMENTS. 


obviated  in  the  terrestrial  telescope  by  the  interposition  of 
two  double  convex  lenses,  m  and  n,  between  the  objective 


FIG.  383. 

and  the  eye-piece.  The  rays,  diverging  from  the  inverted 
image  at  J,  cross  between  rti  and  n  and  form  an  erect, 
magnified,  virtual  image  at  ab. 

Experiment  4. — Reflect  a  horizontal  beam  of  sunlight  into  a 
darkened  room.  In  its  path,  place  a  piece  of  smoked  glass  on  which 
you  have  traced  the  representation  of  an  arrow,  AB  (Fig.  384),  or 


FIG.  384. 

written  your  autograph.  Be  sure  that  every  stroke  of  the  pencil 
has  cut  through  the  lamp  black  and  exposed  the  glass  beneath. 
Place  a  convex  lens  beyond  the  pane  of  glass,  as  at  L,  so  that  rays 
that  pass  through  the  transparent  tracings  may  be  refracted  by  it 
as  shown  in  the  figure.  It  is  evident  that  an  image  will  be  formed 
at  th 3  foci  of  the  lens.  If  a  screen,  88,  be  held  at  the  positions  of 
these  foci,  a  and  6,  the  image  will  appear  clearly  cut  and  bright.  If 
the  screen  be  held  nearer  the  lens  or  further  from  it,  as  at  8'  or  S", 
the  picture  will  be  blurred. 

734.  Magic  Lantern. — In  the  magic  lantern,  a 
lamp  is  placed  at  the  common  focus  of  a  convex  lens  in 
front  of  it  and  of  a  concave  mirror  behind  it.  The  light 
is  thus  concentrated  upon  ab,  a  transparent  picture,  called 
the  "slide."  A  system  of  lenses,  m,  is  placed  at  a  little 


OPTICAL  INSTRUMENTS. 


543 


more  than  its  focal  distance  beyond  the  slide.     A  real, 
inverted,  magnified  image  of   the   picture  is  thus  pro- 


FIG.  385. 

jected  upon  the  screen,  8.  The  tube  carrying  m  is  adjust- 
able, so  that  the  foci  may  be  made  to  fall  upon  the  screen 
and  thus  render  the  image  distinct.  By  inverting  the 
slide,  the  image  is 
seen  right  side  up. 
The  solar  and  elec- 
tric microscopes  act 
in  nearly  the  same 
way,  the  chief  differ- 
ence being  in  the 
source  of  light. 


FIG.  386. 


(a.)  Directions  for 
making  a  simple  magic 
lantern  may  be  found 
on  page  84  of  Mayer  and 
Barnard's  little  book  on  Light.  Fig.  386  represents  a  very  compact 
and  efficient  lantern,  known  as  Marcy's  Sciopticon,  and  furnished  by 
James  W.  Queen  &  Co.  of  Philadelphia. 

735.  Stereoscopic  Pictures. — Close  the  left  eye 
and  hold  the  right  hand  so  that  the  forefinger  shall  hide 


544 


OPTICAL  INSTRUMENTS. 


FIG.  387. 


the  other  three  fingers.  Without  changing  the  position 
of  the  hand,  open  the  left  and  close  the  right  eye.  The 
hidden  fingers  become  visible  in  part.  Place  a  die  on  the 
table  directly  in  front  of  you.  Looking  at  it  with  only  the 
left  eye,  three  faces  are  visible,  as  shown  at  A,  Fig.  387. 

Looking  at  it  with  only  the 
right  eye,  it  appears  as  shown 
at  B.  From  this  we  see  that 
when  we  look  at  a  solid,  the 
images  upon  the  retinas  of 
the  two  eyes  are  different. 

If,  in  any  way,  we  combine  two  drawings,  so  as  to  produce 
images  upon  the  retinas  of  the  two  eyes  like  those  produced 
by  the  solid  object,  we  obtain  the  idea  of  solidity. 


736.  The  Stereoscope.— To  blend  these  two  pic- 
tures is  the  office  of  the  stereoscope.  Its  action  will  be 
readily  understood  from  Fig.  388.  The 
diaphragm,  D,  prevents  either  eye  from 
seeing  both  pictures  at  the  same  time. 
Rays  of  light  from  B  are  refracted  by 
the  half -lens  E'  so  that  they  seem  to 
come  from  C.  In  the  same  way,  rays 
from  A  are  refracted  by  E  so  that 
they  also  seem  to  come  from  C.  The 
two  slightly  different  pictures  thus 
seeming  to  be  in  the  same  place  at  the 
same  time  are  successfully  blended ; 
the  picture  "stands  out,"  or  has  the 
appearance  of  solidity.  If  the  two 
pictures  of  a  stereoscopic  view  were  exactly  alike,  this 
impression  of  solidity  would  not  be  produced. 


FIG. 


P  OLA  RIZA  TION.  545 

737.  Polarization.— If  a  horizontal  string,  tightly 
drawn,  be  hit  a  vertical  blow,  a  wave  will  be  formed  with 
vibrations  in   a  vertical  plane.    If  the   string  be  hit  a 
horizontal  blow,  a  wave  will  be  formed  with  vibrations  in 
a  horizontal  plane.     Thus  a  transversal  wave  is  capable  of 
assuming  a  particular  side  or  direction  while  a  longitudinal 
wave  is  not.    This  is  expressed  by  saying  that  a  transversal 
wave  is   capable   of  polarization.      Polarization  of  light 
may  be  produced  in  three  ways — by  absorption,  by  reflec- 
tion and  by  double  refraction. 

(a.)  Polarized  light  presents,  to  the  naked  eye,  the  same  appear- 
ance as  common  light.  In  polarization  experiments,  two  pieces  of 
apparatus  must  generally  be  employed  ;  one  to  produce  polariza- 
tion ;  the  other  to  show  it.  The  former  is  called  the  polarizer;  the 
latter,  the  analyzer.  Apparatus  that  serves  for  either  of  these  pur- 
poses will  also  serve  for  the  other. 

738.  Planes  of  Vibration  in  Sunbeam.— If 

we  imagine  a  sunbeam  to  be  cut  by  a  plane  perpendicular 
to  the  direction  of  the  beam,  we  may  sup- 
pose  the   section   to   consist    of    vibrations 
moving  in  every  possible   plane,   as  repre- 
sented  by  Fig.   389.     It   is  not  to  be  sup- 
posed that  all  of  these  planes  will  intersect 
at  the  same  point.     There  will  be  many  rays 
whose  planes  of  vibration  are  vertical,  many  whose  planes 
of  vibration  are  horizontal,  etc. 

739.  Polarization  by  Absorp- 
tion.— If  a  sunbeam  fall  upon  a  substance 
whose  molecular  structure  allows  vibrations 
in  only  a  particular  plane,  say  vertical,  the 
substance  may  be  compared  to  a  frame  with 
FIG.  390.  vertical  bars,  as  represented  by  Fig.  390, 


546  P  OLARIZA  TION. 

Such  a  frame  or  such  a  substance  will  absorb  the  rays 
whose  vibrations  lie  in  a  plane  that  is  horizontal  or  nearly 
so,  convert  them  into  absorbed  heat  and  transmit,  as 
polarized  light,  those  rays  whose  vibrations  lie  in  a  plane 
that  is  vertical  or  nearly  so.  A  plate  cut 
in  a  certain  way  from  a  crystal  of  tour- 
maline acts  in  such  a  way ;  it  is  called  a 
tourmaline  analyzer.  If  the  sunbeam  fall 
upon  a  substance  that  allows  vibrations 

in  only  a  horizontal  plane,  the  substance 
FIG.  39  r. 

may  be  compared  to  a  frame  with  hori- 
zontal bars,  as  represented  in  Fig.  391.  Such  a  body  will 
quench  all  the  rays  whose  vibrations  lie  in  a  plane  that  is 
vertical  or  nearly  so  and  transmit,  as  polarized  light,  those 
rays  whose  vibrations  lie  in  a  plane  that  is  horizontal  or 
nearly  so.  The  tourmaline  analyzer  previously  used  acts 
in  this  way  when  turned  a  quarter  way  around. 

74O.  Tourmaline  Tongs. — If  these  two  frames,  or 
two  tourmaline  analyzers,  be  placed  one  over  the  other  in 
such  a  way  that  the  bars  of  the  second  shall  be  perpen- 
dicular to  those  of  the 
first,  it  will  be  seen  that 
the  first  will  quench  or 

absorb  part  of  the  rays, 

J  '  FIG.  392. 

while  the  rays  trans- 
mitted by  the  first  as  polarized  light  will  be  quenched  by 
the  second.  But  if  the  bars  of  the  second  be  parallel  to 
those  of  the  first,  the  polarized  light  transmitted  by  the 
first  will  also  be  transmitted  by  the  second.  This  partial 
or  total  absorption  of  luminous  rays  is  shown  easily  with 
the  "  tourmaline  tongs,"  which  consist  of  two  tourmaline 


POLARIZATION. 


547 


FIG.  393- 


plates  set  in  movable  discs  (Fig.  392).  Light  transmitted 
by  either  plate  is  polarized  (and  colored  by  the  accidental 
tint  of  the  tourmaline).  When  the  plates  are  superposed, 
polarized  light  may  be  transmitted  by  both,  or  all  of  the 
incident  light  may  be  absorbed  according  to  their  relative 
positions  as  above  stated. 

741.  Polarization  by  Reflection. — Light  is 
polarized  when  the  rays  whose 
vibrations  lie  in  a  particular 
plane  are  alone  allowed  to  pass. 
This  effect  may  be  produced  by 
causing  a  beam  of  light  to  be 
reflected  by  a  non-metallic  mirror 
at  a  certain  angle  which  depends 
upon  the  nature  of  the  reflecting 
substance.  For  glass,  the  ray 
must  make  with  the  reflecting  surface  an  angle  of  35°  25' 
(angle  of  incidence  =  54°  35'). 

742.  Malus's  Po- 
lariscope. — This  in- 
strument has  two  reflec- 
tors made  of  bundles  of 
glass  plates.  (An  ordi- 
nary looking-glass  is  a 
metallic  mirror.)  Of 
these,  A  is  called  the 
polarizer  and  B  the 
analyzer.  Both  reflec- 
tors turn  upon  horizon- 
tal axes;  B  also  turns 
vertical  axis  by  means  of  the  horizontal  circles,  (7(7, 


FIG.  395. 


548  P  OLARIZA  TION. 

When  A  and  B  are  placed  at  the  polarizing  angle  with 
the  vertical  axis,  a  beam  of  light  is  made  to  fall  upon  the 
polarizer  in  such  a  direction  that  the  reflected  light  will 
pass  vertically  upward  to  B.  This  reflected  light  will  be 
polarized.  The  polarized  light  will  be  reflected  by  B 
when  the  second  reflector  is  parallel  to  the  first  (Fig.  395); 
it  will  be  absorbed  or  transmitted  when  B  is  perpendicular 
to  A  (Fig.  394). 

(a.)  Place  B  as  shown  in  Fig.  395.  Throw  a  beam  of  light  upon 
A,  the  room  being  darkened.  The  light  reflected  from  B  will  form 
a  white  spot  upon  the  side  of  the  room.  Turn  the  collar,  C,  slowly 
around.  The  spot  of  light  will  move  around  the  sides  of  the 
room,  gradually  growing  fainter.  When  G  has  been  turned  a 
quarter  way  around  (Fig.  394),  the  spot  has  wholly  disappeared. 
Beyond  this  it  grows  brighter  until  G  has  been  turned  half  way 
around,  when  it  is  as  bright  as  at  the  beginning.  When  C  has 
been  turned  three-quarters  around,  the  spot  again  disappears, 
again  reappearing  as  G  and  B  are  brought  to  their  original 
positions. 

743.  Double  Refraction. — A  crystal  of  Iceland 
spar  shows  a  very  important  effect  upon  an  incident 

beam.  The  retarda- 
tion of  the  vibrations 
whose  plane  is  paral- 
lel to  the  axis  (the 
line  joining  the  two 
obtuse  angles  of  the 
crystal)  is  different 

FIG      ,  from   the  retardation 

of      the     vibrations 

whose  plane  is  perpendicular  to  the  axis.  This  differ- 
ence in  change  of  velocity  produces  a  difference  in  the 
refraction  of  the  two  sets  of  rays.  A  beam  of  light, 


OPTICAL  INSTRUMENTS.  549 

therefore,  falling  upon  a  crystal  of  Iceland  spar  will  be 
generally  split  into  two,  producing  the  effect  known  as 
double  refraction. 

(a.)  A  small  object,  as  a  dot  or  line,  viewed  through  a  crystal  of 
Iceland  spar,  will  generally  show  two  images  formed  by  light  oppo- 
sitely polarized.  If  the  eye  be  placed  directly  above  the  dot  and 
the  crystal  be  slowly  turned  around,  one  image  known  as  the  ordinary 
image  will  remain  stationary,  while  the  other  known  as  the  extra- 
ordinary image  will  revolve  about  it  at  a  varying  distance.  The 
ordinary  ray  has  a  constant  and  the  extraordinary  ray  a  variable 
index  of  refraction. 

(6.)  On  looking,  through  a  tourmaline  or  any  other  analyzer,  at 
the  two  images  formed  by  double  refraction,  it  will  be  found  that 
there  is  a  marked  difference  in  the  brightness  of  the  two  images. 
As  the  analyzer  is  turned  around,  one  image  grows  brighter  and  the 
other  fainter,  the  greatest  brightness  of  one  being  simultaneous 
with  the  extinction  of  the  other. 


744.   Nicol's   Prism. — One  of  the  most  valuable 
pieces  of  polarizing  apparatus  is  Nicol's  prism.     A  crystal 


FIG.  397. 

of  Iceland  spar  is  bisected  in  a  plane,  AB,  passing  through 
its  two  obtuse  angles,  as  shown  in  the  figure.  The  two 
halves  are  then  cemented  in  their  original  position  with 
Canada  balsam.  The  refractive  power  of  the  balsam  is 
such  that  the  extraordinary  ray  passes  through  it  at  E, 
while  the  ordinary  ray,  striking  the  balsam  at  an  angle 
greater  than  its  critical  angle,  is  reflected  at  N,  passes  out 


550 


OPTICAL  INSTRUMENTS. 


of  the  crystal  and  is  then  absorbed  by  the  surrounding 
frame  of  the  prism.  Since  the  "  Nicol  "  allows  only  the 
extraordinary  ray  to  pass,  it  may  be  used,  like  a  tourmaline, 
as  an  analyzer  or  as  a  polarizer. 

(a.)  When  the  light  of  the  blue  sky  is  looked  at  through  a  Nicol 
or  other  analyzer  (at  an  angular  distance  of  90°  from  the  sun),  a  dif- 
ference of  brightness  is  seen  as  the  analyzer  is  turned.  The  degree 
of  difference  between  the  maximum  and  the  minimum  of  light  thus 
observed  measures  the  degree  in  which  such  light  is  polarized. 


FIG.  398. 


745.  A  Simple  Polariscope. — In  the  accompany- 
ing figure,  B  is  a  pile  of  six  or  eight  glass  plates  about 

15  cm.  square,  serving  as 
a  polarizer.  A  Nicol  at 
E  serves  as  an  analyzer. 
The  Nicol  is  supported, 
as  shown  in  the  figure,  so 
as  to  view  the  centre  of 
the  polarizer  at  the  polar- 
izing angle  of  glass.  The 
prism  should  be  mounted 
so  that  it  may  be  turned  on  its  axis  in  its  support.  G  is 
a  piece  of  ground  glass  for  cutting  off  the  images  of 
outside  objects.  The  object  to  be  examined  is  placed  on 
the  glass  table  or  shelf,  T.  The  instrument  is  placed  with 
G  facing  a  window  and  covered  with  a  cloth  to  cut  off 
unpolarized  light. 

(a.)  Place  a  thin  plate  (film)  of  mica  or  selenite  on  the  table,  T, 
and  look  through  the  Nicol  while  you  turn  it  about  on  its  axis.  A 
beautiful  display  of  colors  is  seen,  each  reaching  its  maximum  brill- 
iancy, fading  away  and  changing  to  its  complementary  color  as  the 
analyzer  is  turned.  The  colors  and  changes  of  color  are  due  to 
the  interference  of  polarized  rays. 


RECAPITVLA  TlOtf. 


551 


Recapitulation. — To  be  amplified  by  tbe  pupil  for 
review. 

f  OBSCURA. 

CAMERA J 

I  PHOTOGRAPHER'S. 

HUMAN   EYE   AND   ITS   ACTION. 

r  SIMPLE. 


en 


MICROSCOPES 


TELESCOPES 


COMPOUND. 
REFLECTORS. 

REFRACTORS  

GALILEAN. 
OPERA  GLASS. 
ASTRONOMICAL 
TERRESTRIAL, 

MAGIC  LANTERN. 
STEREOSCOPE. 


POLARIZATION 


BY  ABSORPTION. 

BY  REFLECTION. 

BY  DOUBLE  REFRACTION. 

POLARISCOPES. 


552  ENERGY. 


CONCLUSION. 

ENERGY. 

746.  Solar  Energy. — The  work  performed  by  men 
and  other  animals  is  due  to  the  transformed  energy  of  food. 
"  This  food  is  of  vegetable  origin  and  owes  its  energy  to 
the  solar  rays.     The  energy  of  men  and  animals  is,  there- 
fore, the  transformed  energy  of  the  sun.     Excepting  the 
energy  of  the  tides,  the  sun's  rays  are  the  source  of  all  the 
forms  of  energy  practically  available.     It  has  been  esti- 
mated that  the  heat  received  by  the  earth  from  the  sun 
each  year  would  melt  a  layer  of  ice  over  the  entire  globe 
a  hundred   feet  in   thickness.      This  represents    energy 
equal  to  one  horse-power  for  each   fifty  square  feet  of 
surface." 

747.  Dissipation  of  Energy.— "It  has  been  seen 
that  only  a  fraction  of  the  energy  of  heat  is  available  for 
transformation  into  other  forms  of  energy  and  that  such 
transformation  is  possible  only  when  a  difference  of  tem- 
perature  exists.      Every  conversion  of  other  forms  of 
energy  into  heat  puts  it  in  a  form  from  which  it  can  be 
only  partially  recovered.     Every  transfer  of  heat  from  one 
body  to  another,  or  from  one  part  to  another  of  the  same 
body,  tends  to  equalize  temperatures  and   diminish   the 
proportion  of  energy  available  for  transformation.     Such 
transfers  of  heat  are  continually  taking  place  ;  and,  as  far 
as  our  present  knowledge  goes,  there  is  a  tendency  toward 
an  equality  of  temperature,  or,  in  other  words,  a  uniform 


ENERGY.  553 

molecular  motion,  throughout  the  universe.  If  this  con- 
dition of  things  were  reached,  although  the  total  amount 
of  energy  existing  in  the  universe  would  remain  un- 
changed, the  possibility  of  transformation  would  be  at  an 
end  and  all  activity  and  change  would  cease.  This  is  the 
doctrine  of  the  dissipation  of  energy  to  which  our  limited 
knowledge  of  the  operations  of  nature  leads  us;  but  it 
must  be  remembered  that  our  knowledge  is  very  limited 
and  that  there  may  be  in  nature  the  means  of  restoring 
the  differences  upon  which  all  activity  depends." — Anthony 
and  Braclcett. 

748.  Varieties  of  Energy. — Like  matter,  energy 
is  indestructible.    We  have  already  seen  that  energy  may 
oe  visible  or  invisible   (i.  e.,  mechanical  or  molecular), 
kinetic  or  potential.     "We  have  at  our  control  at  least 
eight  varieties  of  energy. 

(a.)  Mechanical  energy  of  position  (visible,  potential). 
(&.)  Mechanical  energy  of  motion  (visible,  kinetic). 
(e.)  Latent  heat  (molecular,  potential). 
(d.)  Sensible  heat  (molecular,  kinetic). 
(e.)  Chemical  separation  (molecular  or  atomic  ;  potential). 
(/.)  Electric  separation  (probably  molecular,  potential). 
(g.)  Electricity  in  motion  (probably  molecular,  kinetic). 
(h.)  Radiant  energy,  thermal,   luminous  or  actinic  (molecular, 
kinetic). 

749.  Conservation  of  Energy.— The  doctrine 
that;  considering  the  universe  as  a  whole,  the  sum  of  ah 
these  forces  is  a  constant  quantity,  is  known  as  the  Con- 
servation of  Energy. 

a  +  b  +  c  +  d  +  e+f  +  g  +  h  =  &  constant  quantity. 

This  does  not  mean  that  the  value  of  a  is  invariable ;  we 
have  seen  it  changed  to  other  varieties  as  b  or  d. "  We  have 


554  ENtittQY. 

seen  heat  changed  to  electricity  and  vice  versa,  and  eithef 
or  both  changed  to  mechanical  energy.  It  does  not  mean 
that  the  sum  of  these  eight  variable  quantities  in  the  earth 
is  constant,  for  we  have  seen  that  energy  may  pass  from 
sun  to  earth,  from  star  to  star.  But  it  does  mean  that  the 
sum  of  all  these  energies  in  all  the  worlds  that  constitute 
the  universe  is  a  quantity  fixed,  invariable. 

750.  Correlation  of  Energy.— The  expression 
Correlation  of  Energy  refers  to  the  convertibility  of  one 
form  of  energy  into  another.     Our  ideas  ought,  by  this 
time,  to  be  clear  in  regard  to  this  convertibility.    One  im- 
portant feature  remains  to  be  noticed.    Eadiant  energy  can 
be  converted  into  other  forms,  or  other  forms  into  radiant 
energy  only  through  the  intermediate  state  of  absorbed 
beat. 

751.  A  Prose  Poem.—"  A  river,  in  descending  from  an 
elevation  of  7720  feet,  generates  an  amount  of  heat  competent  to 
augment  its  own  temperature  10°  F.,  and  this  amount  of  heat  was 
abstracted  from  the  sun,  in  order  to  lift  the  matter  of  the  river  to 
the  elevation  from  which  it  falls.     As  long  as  the  river  continues 
on  the  heights,  whether  in  the  solid  form  as  a  glacier,  or  in  the 
liquid  form  as  a  lake,  the  heat  expended  by  the  sun  in  lifting  it 
has  disappeared  from  the  universe.     It  has  been  consumed  in  the 
act  of  lifting.     But,  at  the  moment  that  the  river  starts  upon  its 
downward  course,  and  encounters  the  resistance  of  its  bed,  the  heat 
expended  in  its  elevation  begins  to  be  restored.     The  mental  eye, 
indeed,  can  follow  the  emission  from  its  source  through  the  ether, 
as  vibratory  motion,  to  the  ocean,  where  it  ceases  to  be  vibration, 
and  takes  the  potential  form  among  the  molecules  of  aqueous  vapor  ; 
to  the  mountain  top,  where  the  heat  absorbed  in  vaporization  is  given 
out  in  condensation,  while  that  expended  by  the  sun  in  lifting  the 
water  to  its  present  elevation  is  still  unrestored.     This  we  find  paid 
back  to  the  last  unit  by  the  friction  along  the  river's  bed ;  at  the 
bottom  of  the  cascade,  where  the  plunge  of  the  torrent  is  suddenly 
arrested  ;  in  the  warmth  of  the  machinery  turned  by  the  river  ;  in 
the  spark  from  the  millstone  ;  beneath  the  crusher  of  the  miner ;  ia 


555 


the  Alpine  saw-mill ;  in  the  milk-churn  of  the  chalet ;  in  the  sup- 
ports of  the  cradle  in  which  the  mountaineer,  by  water-power,  rocks 
his  baby  to  sleep.  All  the  forms  of  mechanical  motion  here  indi- 
cated are  simply  the  parcelling  out  of  an  amount  of  calorific  motion 
derived  originally  from  the  sun  ;  and,  at  each  point  at  which  the 
mechanical  motion  is  destroyed  or  diminished,  it  is  the  sun's  heat 
,vhich  is  restored." — TyndalL 


o 


w 


Recapitul  ation . 

f  VISIBLE    OR    MECHANICAL. 

SOURCE. 
DISSIPATION. 


J   OF  POSITION,  e.  g.,  Hanging  Ap- 
Potential.          pie,     Head    of 


INVISIBLE   OR 
MOLECULAR. 


HEAT. 


LIGHT 


ELECTRICITY...  4 


Water. 


OF  MOTION,  e.  g.,  Falling  Apple, 
^      Kinetic.  Flowing  Water. 

OF  POSITION,  e.  g.,  Latent  Heat. 
Potential. 

OF  MOTION,  e.  g.,  Sensible  Heat. 
Kinetic. 

OF  MOTION,  or 
Kinetic. 

OF  POSITION,  e.  g.,  Charged  Ley* 
Potential.  den  jar,  Batter  j 

•with  circuit  bro- 
k,n. 


OF  MOTION,  e.  g.,  Ley  den  jar  dis- 
Kinetic.  charging:   Bat- 

tery   with   cir- 
cuit closed. 


GENERAL  REVIEW. 

1.  (a.)  Define  science,  matter,  mass,  molecule  and  atom.     (&.)  How 
do  physical  and  chemical  changes  differ  ?    (c.)  Define  physics. 

2.  (a.)  What  are  chemical  and  physical  properties  of  matter? 
(&.)    Define  and  illustrate  two  universal  and    one    characteristic 
properties  of  matter. 

3.  (a.)  Define  meter,  liter  and  gram.     (&.)  What  is   a  solid,  a 
liquid,  and  a  gas  ?    (c.)  Define  dynamics  and  force. 

4.  (a.}  Name  and  define  three  units  of  force.     (&.)  Give  Newton's 
Laws  of  Motion,     (c.)  Give  the  law  of  reflected  motion. 


,5-56  REVIEW. 

5.  (a.)  Explain  the  parallelogram  of  forces,  and  (6.)  the  polygon 
of  forces. 

6.  (a.)  Define  gravitation  and  give  its  laws.    (6.)  Give  the  law  of 
weight,     (c.)  What  is  the  centre  of  gravity,  and  how  may  it  be 
found  ? 

7.  (a.)  Describe   Att  wood's  machine.      (6.)    Give  the  rules  and 
formulas  for  falling  bodies,     (c.)  How  far  will  a  body  fall  in  three 
seconds  ? 

8.  (a.)  What  is  a  pendulum  ?    (&.)  Give  the  laws  of  the  pendulum. 
(c.)  How  long  must  a  pendulum  be  to  vibrate  10  times  a  minute  ? 

9.  (a.)  Define  energy,   foot-pound,  dyne,  erg,  and  horse-power. 
(b.)  Deduce  the  formula  for  measuring  kinetic  energy  when  weight 
and  velocity  are  given. 

10.  («.)  Define  each  of  the  six  traditional  simple  machines.     (&.) 
Give  the  law  for  each,     (c.)  What  is  the  office  of  a  machine  ?    (d.\ 
Discuss  the  subject  of  friction. 

11.  (a.)  Give  Pascal's  law,  and  the  rule  for  determining  lateral 
liquid  pressure.    (&.)  Describe  the  hydrostatic  press,  and  state  the 
general  principle  upon  which  its  action  depends. 

12.  (a.)  State  Archimedes'  principle.    (6.)  What  is  specific  gravity  ? 
(c.)  Explain  the  determination  of  the  sp.  gr.  of  a  solid  lighter  than 
water,     (d.)  Explain  the  use  of  the  specific  gravity  bulb,      (e.) 
Describe  Nicholson's  hydrometer  and  explain  its  use. 

13.  (a.)  A  1000  gr.  bottle  having  in  it  928  grs.  of  water,  has  the 
remaining  space  filled  with  metallic  sand  and  then  weighs  1126.75. 
What  is  the  sp.  gr.  of  the  sand  ?    (6.)  Through  which  of  the  three 
kinds  of  levers  can  the  greatest  power  be  gained  ?    (c.)  Through 
which  can  none  be  gained  ?    (d.)  Why  do  we  use  it  ?    (e.)  Give  an 
example. 

14.  A  ball  projected  vertically  upward,  returns  in  15  seconds  to 
the  place  of  projection.    How  far  did  it  ascend  ? 

15.  (a.)  A  floating  solid  displaces  how  much  liquid?    (&.)  An 
immersed  solid  displaces  how  much  liquid  ?    (c.)  A  floating  solid 
loses  how  much  weight  ?    (d.)  An  immersed  solid  loses  how  much 
weight  ? 

16.  What  is  the  energy  of  a  rifle-ball  weighing  32  grains,  having 
a  velocity  of  213  meters  per  second,  and  striking  in  the  centre  of  a 
pendulum  of  wood  weighing  23  kilograms  ? 

17.  (#.)  What  is  meant  by  the  increment  of  velocity  or  gravity  ? 
(6.)  How  far  will  a  body  fall  in  6|  seconds?    (c.)  How  far  in  the 
9th  second  ?    (d.)  If  a  freely-falling  body  have  a  velocity  of  448  ft. 
per  second,  how  long  has  it  been  falling  ? 

18.  (a.)  Deduce,  from  the  laws  of  falling  bodies,  the  formula  for 


REVIEW.  557 

the  velocity  of  spouting  liquids  (t>  =  8.02  /y/A).  (&.)  Why  must  the 
unit  of  measure  used  with  this  formula  be  feet?  (c.)  Deduce  a 
similar  formula  in  which  the  meter  is  involved  as  the  unit. 

19.  Name  four  kinds  of  water-wheels,  and  describe  the  most 
efficient  of  them. 

20.  (a.}  Explain  the  action  of  the  mercury  barometer.    (6.)  Give 
Mariotte's  law.    (c.)   Describe  the  piston  of  Sprengel's  air-pump. 
(d.)  Describe  the  ordinary  air-pump,     (e.)  Explain  the  action  of  the 
siphon. 

21.  (a.)  How  would  you  illustrate  the  law  of  magnetic  attraction 
and  repulsion?    (&.)    Give  the  theory  of  magnetism,     (c.)  Explain 
the  action  of  the  electrophorus ;  what  do  you  think  of  its  accuracy 
and  value  ?    (d.)  Explain  terrestrial  induction. 

22.  If  the  capacity  of  the  barrel  of  an  air-pump  be  \  that  of  the 
receiver,  how  much  air  would  remain  in  the  receiver  at  the  end  of 
the  fourth  stroke  of  the  piston,  and  what  would  be  its  tension 
compared  with  that  of  the  external  air  ? 

23.  What  is  the  pressure  on  the  side  of  a  reservoir  150  feet  long, 
and  filled  with  water  to  the  height  of  twenty  feet  ? 

24.  (a.)  Why  is  a  reservoir  usually  built  in  connection  with 
water- works  ?     (&.)   Why  are  fire-engines  provided  with  an  air- 
chamber?      (c.)    Why  should    the    nozzle    be    smaller   than    the 
hose? 

25.  (a.)  Why  can  you  not  raise  water  50  feet  with  a  common 
pump  ?    (6.)  What  change  would  it  be  necessary  to  make  in  the 
pump  in  order  to  raise  water  to  that  height  ?    (c.)  Illustrate  by  a 
diagram. 

26.  (a.)  Give  the  law  of  electrical  attraction  and  repulsion,  and 
illustrate  by  pith-ball  electroscope.     (6.)  Define  conductors  and  non- 
conductors, electrics  and  non-electrics,     (c.)  Illustrate  by  an  example 
of  each. 

27.  (a.)  Give  and  illustrate  each  of  the  laws  of  motion.    (6.) 
Explain  composition  and  resolution  of    forces   with   illustrative 
figures. 

28.  (a.)  Give  the  facts  of  gravity  and  the  law  of  weight.     (6.) 
If  a  body  weigh  120  Ibs.  2500  miles  below  the  surface  of  the  earth, 
at  what  distance  above  the  surface  will  it  weigh  80  Ibs.  ? 

29.  Explain  and  illustrate  electric  induction  fully. 

30.  (a.)  Explain  the  construction  and  action  of  the  electrophorus. 
What  kind  of  electricity  is  discharged  from  it  ?    (&.)  Describe  the 
Leyden  jar  and  explain  its  action,    (c.)  Explain  the  action  of  the 
plate  electric  machine,     (d.)  In  what  way  do  lightning-rods  protect 
buildings  ? 


558  REVIEW. 

31.  (a.)  Discuss  carefully  the  resistance  of  a  Galvanic  cell.     (b.\ 
Describe  the  Voltaic  arc. 

32.  (a.)  State  the  difference  between  a  magnet  and  an  electro 
magnet.    (5.)  Give  the  principles  on  which  the  telegraph  operates, 
(c.)  What  is  meant  by  an  "  electro  negative  substance  ?  " 

33.  (a.)  Describe  Ruhmkorff  s  coil,  and  (&.)  explain  its  action. 

34.  Describe  the  thermo-electric  pile,  and  explain  its  use. 

35.  (a.)  Give  Prof.  Tyndall's  illustration  of  the  propagation  of 
sound.    (6.)  What  is  the  velocity  of  sound  in  air  ?    (c.)  How  is  it 
affected  by  temperature  ? 

36.  (a.)  Explain  the  difference  between  noise  and  music,     (fc.) 
Name  the  three  elements  of  a  musical  sound,  and  state  the  physical 
cause  of  each. 

37.  (a.)  Describe  and  explain  the  telephone.     (6.)  The  phono- 
graph. 

38.  (a.)   Explain  interference  of  sound.     (6.)   Give  the  laws  of 
vibration  of  musical  strings,     (c.)   Give  the  relative  numbers  of 
vibration  for  the  tones  of  the  major  diatonic  scale. 

39.  (a.)  If  18  seconds  intervene  between  the  flash  and  report  of  a 
gun,  what  is  its  distance,  temperature  being  82°  F.  ?     (6.)    If   a 
musical  sound  be  due  to  144  vibrations  per  second,  how  many 
vibrations  correspond  to  its  3d,  5th,  and  octave  ? 

40.  The  bottom  of  a  tank  is  100  centimeters  on  one  side,  and  a 
meter  on  the  adjoining  side.     The  tank  has  a  depth  of  50  centi- 
meters of  water,     (a.}  What  is  the  pressure  on  the  bottom  ?    (&.) 
On  either  one  of  the  vertical  sides  ? 

41.  (a.)  What  is  a  horse-power?    (6.)  How  many  horse-powers 
are  there  in  a  machine  that  will  raise  8250  Ibs.  176  ft.  in  4  minutes  ? 
(c.)  State  the  modes  of  diminishing  friction. 

42.  What  will  be  the  kinetic  energy  of  a  25-pound  ball  that  has 
fallen  a  mile  ?    (Reject  small  remainders ) 

43.  Two  bodies  are  attracting  a  third  with  forces  as  441  to  576, 
the  first,  weighing  25  Ibs.,  at  a  distance  from  the  third  of  20  feet, 
and  the  second  at  a  distance  of  30  feet ;  what  is  the  weight  of  the 
second  ? 

44  How  far  will  a  body  fall  in  the  first  second  on  Saturn,  the 
density  of  Saturn  being  .12  that  of  the  earth,  and  its  diameter  being 
72000  miles? 

45.  (a.)  What  is  temperature  ?     (6.)   Discuss  the  expansion  of 
water  by  heat,     (c.)  What  is  the  rate  of  gaseous  expansion  by  heat  ? 

46.  (a.)  What  is  the  difference  between  evaporation  and  boiling ''. 
\b.)  What  is  the  boiling  point  ?    (c )  What  is  distillation,  and 

is  it  performed.  ? 


REVIEW.  559 

47.  (a.)  Define  latent,  sensible  and  specific  heat,    ft.)  What  is  the 
latent  heat  of  water  and  of  steam  ? 

48.  (a.)  Explain  the  several  modes  of  diffusing  heat,  showing 
how  they  differ.    (b.)  State  and  explain  the  relation  between  the 
absorbing  and  radiating  powers  of  any  given  substance. 

49.  (a.)    What  is  thermodynamics  ?    (b.)   State  the  first  law  of 
thermodynamics,     (c.)  What  is  the  mechanical  equivalent  of  heav 
in  kilogrammeters  ?    (d.)  What  does  your  answer  mean  ? 

50.  (d.)  Draw  a  figure  showing  the  position  of  the  parts  of  thf 
cylinder  and  steam-chest  when  the  piston  is  going  up. 

51.  (a.)    To  what  temperature   would  a  cannon-ball  weighing 
150  Ibs.  and  moving  1920  feet  a  second,  raise  2000  Ibs.  of  water 
from  32°  F.,  if  its  motion  were  suddenly  converted  into  heat  ?    (&.) 
Explain  the  origin  and  propagation  of  sound  waves. 

52.  (a.)  Express  a  temperature  of  50°  F.  in  degrees  centigrade. 
(b.)  Name  and  describe  the  essential  parts  of  a  steam-engine  in  their 
proper  order,    (c.}  Point  out  the  changes  in  form  of  energy  from 
the  furnace  fire,  through  a  high-pressure  engine  to  the  heated  axles 
set  in  motion  thereby. 

53.  The  mechanical  equivalent  of  heat  being  1390  foot-grams, 
the  foot  being  equal  to  30.48cm.,  and  the  increment  of  velocity  on 
the  earth  being  980  cm. ,  find  the  mechanical  equivalent  in  ergs. 

Am.  41519856. 

54.  (a.)  What  is  the  difference  between  waves  of  sound  and 
waves  of  light  ?    (6.)  What  is  the  difference  between  an  atherma- 
nous  and  an  opaque  substance  ?    (c.)  What  determines  the  apparent 
size  of  a  visible  object  ? 

55.  (a.)  If  the  gun-cotton  mentioned  in  §  620  (a.)  be  rubbed  with 
a  little  lamp-black,  will  it  be  ignited  with  more  or  less  difficulty  ? 
Why?    (b.)  What  is  reflection  of  light?    (c.)  How  does  it  differ 
from  refraction  of  light  ? 

56.  («.)  How  could  you  show  that  light  is  invisible  unless  it  en- 
ters  the  eye?    (&.)  What  determines  the  apparent  position  of  an 
object?     (c.)  What  is  the  distinction  between  real  and  virtual 


57.  (a.)  Describe  and  illustrate  a  construction  for  conjugate  foci 
in  the  case  of  a  concave  mirror.     (6.)  In  the  case  of  a  convex  lens. 
(c.)  What  is  meant  by  the  index  of  refraction  ?    (d.)  Give  the  laws 
for  refraction  of  light. 

58.  («.)  Explain  total  internal  reflection,    (b.}  What  is  meant  by 
dispersion  of  light?    (c.)  What  is  pure  spectrum  and  how  may  it 
be  produced  ?    (d.)  What  are  Fraunhofer's  Lines  and  what  do  they 
indicate?    (e.)  Name  the  prismatic  colors  in  order. 


560  REVIEW. 

59.  (a.)  Why  does  a  certain  piece  of  glass  look  red  when  it  ia 
held  between  a  lamp  and  the  eye?    (b.)  Why  does  it  look  red  when 
the  lamp  is  between  the  glass  and  the  eye  ?    (c.)  Explain  the  suc- 
cession of  colors  in  the  rainbow,     (d.)  What  three  classes  of  rays  in 
a  sunbeam  ? 

60.  (a.)  Describe  the  human  eye  as  an  optical  instrument.   (&.)  The 
3pera-glass.    (c. )  The  terrestrial  telescope,    (d.)  The  stereoscope. 

61.  (a.)  Explain  polarization  of  light  by  absorption,     (&.)   By 
reflection. 

62.  (a.)  Explain  the  action  of  the  siphon.     (&.)  Find  the  volume 
of  a  balloon  filled  with  hydrogen  that  has  a  lifting  power  of  440  Ibs. 
(sp.  gr.  of  air  =  14.42.     One  liter  of  hydrogen  weighs  .0896  g.) 

63.  («.)  The  barrel  of  an  air-pump  is  $  that  of  the  receiver ;  find 
the  tension  of  the  air  in  the  receiver  after  8  strokes  of  the  piston,  call- 
ing the  normal  pressure  15  Ibs.  and  disregarding  the  capacity  of  the 
connecting  pipes.     (&.)  A  stone  let  fall  from  the  top  of  a  cliff  was 
seen  to  strike  the  bottom  in  6|  seconds  ;  how  high  was  the  cliff  ? 

64.  (a.)  A  ship  passing  from  the  sea  into  a  river,  discharges  44800 
Ibs.  of  cargo,  and  is  found  to  sink  in  the  river  to  the  same  mark  as 
in  the  sea.  The  sp.  gr.  of  sea-water  being  1.028,  find  the  weight  of  the 
ship  and  cargo.    (&.)  A  body  weighing  12  Ibs.  (sp.  gr.  =  ^,)is  fastened 
to  the  bottom  of  a  vessel  by  a  cord.     Water  being  poured  in  until 
the  body  is  covered,  find  the  tension  of  the  cord. 

65.  (a.)  A  current  of  9  amperes  worked  an   arc   electric  light. 
(§  467.)     The  difference  of  potential  between  the  carbon  tips  was 
measured  by  an  electrometer  and  found  to  be  140  volts.     What 
horse-power  was  absorbed  ou  the  arc?     (&.)  Find  the  maximum 
weight  that  can  be  supported  by  a  hydraulic  elevator  connected 
with  a  reservoir,  the  area  of  the  piston  being  24  sq.  in.  and  the 
reservoir  being  170  ft.  above  the  cylinder,     (c.)  The  difference  be- 
tween the  fundamental  tones  of  two  organ -pipes  of  the  same  length, 
one  of  which  is  closed  at  the  top,  is  an  octave.     Explain  why. 

66.  If  the  force   of  gravity  be  taken   as  980   dynes,   and   the 
mechanical  equivalent  of  heat  be  424  grammeters,  what  will  be  the 
value  of  a  lesser  calorie  in  ergs?  Ans.  41,552,000  ergs. 


iir 


j 

APPENDIX   A. 

Mathematical  Formulas. 

TT  —  3.14159.  I  Circumference  of  circle  =  TT  D. 

Area  of  a  circle  =  TT  R2.  |  Surface  of  a  sphere  =  4  TT  R2  =  TT  D*. 

Volume  of  a  sphere  =  ^  TT  R3  =  1  TT  D*. 

APPENDIX    B. 

Soldering. — The  teacher  or  pupil  will  often  find  it  very  con- 
venient to  be  able  to  solder  together  two  pieces  of  metal.  The  pro- 
cess here  described  is  very  simple  and  will  answer  in  most  cases. 
A  bit  of  soft  solder,  the  size  of  a  hazlenut,  may  be  had  gratis  of  any 
good  natured  tinsmith  or  plumber.  Cut  this  into  bits  the  size  of  a 
grain  of  wheat  and  keep  on  hand.  Dissolve  a  teaspoonful  of  zinc 
chloride  (muriate  of  zinc)  in  water  and  bottle  it.  It  may  be  labelled 
"soldering  fluid."  If  you  have  not  a  spirit-lamp  obtain  one,  or 
make  one.  A  small  bottle  (such  as  those  in  which  school-inks  are 
commonly  sold)  will  answer  your  purpose.  Get  a  loosely  fitting  cork 
and  through  it  pass  a  metal  tube  about  an  inch  long  and  the  size  of 
an  ordinary  lead  pencil.  Through  this  tube,  pass  a  bit  of  candle 
wicking.  Fill  the  bottle  with  alcohol,  insert  the  cork,  with  tube 
and  wick,  and  in  a  few  minutes  the  lamp  is  ready.  Having  novf 
the  necessary  materials  you  are  ready  for  work.  For  example,  sup- 
pose that  you  are  to  solder  a  bit  of  wire  to  a  piece  of  tinned  ware. 
If  the  wire  be  rusty,  scrape  or  file  it  clean  at  the  place  of  joining. 
By  pincers  or  in  any  convenient  way  hold  the  wire  and  tin  together. 
Put  a  few  drops  of  "  soldering  fluid"  on  the  joint,  hold  the  tin  in 
the  flame  so  that  the  wire  shall  be  on  the  upper  side,  place  a  bit  of 
solder  on  the  joint  and  hold  in  position  until  the  solder  melts.  Re- 
move from  the  flame  holding  the  tin  and  wire  together  until  the 
solder  has  cooled.  The  work  is  done.  If  you  have  a  "soldering- 
iron,"  you  can  do  a  wider  range  of  work,  as  many  pieces  of  work 
cannot  be  held  in  the  lamp  flame. 

In  soldering  electric  wires,  do  not  use  the  "  soldering  fluid  "  above 
mentioned.  Twist  the  wires  together,  heat  the  joint  in  the  lamp  flame, 
dip  it  into  powdered  rosin  and  then  into  coarse  filings  of  solder,  and 
hold  it  in  the  flame  again  until  the  adhering  solder  melts  and  "  runs," 


562  APPENDIX. 


APPENDIX   C. 

A  copy  of  the  lecture  of  Prof.  Crookes  on  "  Radiant  Matter " 
(§  59  6.)  may  be  obtained  of  JAMES  W.  QUEEN  &  Co.,  Philadelphia, 
for  25  cents.  Teacher  and  pupils  should  secure  one  or  more  copies. 
The  theory  and  experiments  are  alike  beautiful,  interesting  and 
instructive.  In  concluding  the  lecture,  Prof.  Crookes  said  : 

' '  In  studying  this  Fourth  State  of  Matter,  we  seem  at  last  to 
have  within  our  grasp  and  obedient  to  our  control  the  little  indi- 
visible particles  which,  with  good  warrant,  are  supposed  to  consti- 
tute the  physical  basis  of  the  universe.  We  have  seen  that,  in  some 
of  its  properties,  Radiant  Matter  is  as  material  as  this  table,  whilst 
in  other  properties  it  almost  assumes  the  character  of  Radiant 
Energy.  We  have  actually  touched  the  border  land  where  Matter 
and  Force  seem  to  merge  into  one  another,  the  shadowy  realm 
between  Known  and  Unknown." 

APPENDIX   D. 

Prince  Rupert  Drops. — A  neat  illustration  of  the  trans- 
mission of  pressure  by  liquids  (§  216),  may  be  given  by  filling  a 
small  bottle  with  water,  holding  a  Prince  Rupert  drop  in  its  mouth, 
and  breaking  off  the  tapering  end.  The  whole  "drop"  will  be 
instantly  shattered  and  the  force  of  the  concussion  transmitted  in 
every  direction  to  the  bottle  which  will  be  thus  broken.  These 
"  drops"  are  not  expensive  ;  they  may  be  obtained  from  James  W. 
Queen  &  Co.,  924  Chestnut  street,  Philadelphia. 

APPENDIX   E. 

Difference  between  Theory  and  Practice.— The  re- 
sults mentioned  in  §  256  are  never  fully  attained  in  practice.  Only 
the  particles  near  the  centre  of  the  jet  attain  the  theoretical  velocity. 
Further  than  this,  if  we  carefully  examine  the  stream  we  shall 
notice  that  at  a  little  distance  from  the  orifice  the  stream  is  not  more 
than  two-thirds  or  three-fourths  the  size  of  the  orifice.  This  is  duo 
to  the  fact  that  the  liquid  particles  come  from  all  sides  of  the 
opening  and  thus  flow  in  different  directions,  forming  cross  currents, 
which  may  be  seen  if  there  are  solid  particles  floating  in  the  water. 
These  cross  currents  impede  the  free  flow  and  diminish  the  volume 
of  liquid  discharged.  Short  cylindrical  or  funnel-shaped  tubes  in- 
crease the  actual  flow.  In  a  cylindrical  tube,  this  narrowing  of  the 
jet  could  not  take  place  without  forming  a  vacuum  around  the  nar- 


APPENDIX.  563 

row  neck  (called  the  vena  contracta).  The  pressure  of  the  atmos- 
phere,  tending  to  prevent  this  formation  of  such  a  vacuum,  increases 
the  velocity  and  the  volume  of  the  discharge.  The  funnel-shaped 
tube  prevents  the  formation  of  cross  currents  by  leading  the  liquid 
more  gradually  to  the  point  of  exit. 

APPENDIX  P. 

Barker's  Mill. — A  working  model  of  this  apparatus  (§  264) 
may  be  easily  made  by  any  wide-awake  pupil.  Select  a  long,  sound 
lamp-chimney  and  a  fine-grained  cork  that  snugly  fits  the  lower  end. 
Take  a  piece  of  glass  tubing,  the  size  of  a  lead  pencil,  heat  it  intensely 
in  an  alcohol  or  gas  flame  until  you  melt  off  a  piece  a  little  shorter 
than  the  lamp  chimney.  By  reheating  the  end  thus  closed  by 
fusion,  you  may  give  it  a  neat,  rounded  finish.  Prepare  four  pieces 
of  glass  tubing,  each  12  cm.  long.  These  pieces  would  better  be 
made  of  tubing  smaller  than  that  just  used.  To  cut  the  tube  to  the 
desired  length,  scratch  the  glass  at  the  proper  point  with  a  tri- 
angular file,  hold  the  tube  in  both  hands,  one  hand  on  each  side  of 
the  mark  just  made,  knuckles  uppermost  and  thumb-nails  touching 
each  other  at  a  point  on  the  tube  directly  opposite  the  file-scratch, 
push  with  the  thumbs  and  at  the  same  time  pull  with  the  fingers. 
The  tube  will  break  squarely  off  Smooth  the  sharp  edges  by  soft- 
ening in  the  alcohol  flame.  Bend  each  of  these  four  pieces  at  right 
angles,  2  cm.  from  each  end,  in  such  a  way  that  one  of  the  short 
arms  may  be  in  a  horizontal  plane  while  the  other  short  arm  of  the 
same  piece  is  in  a  vertical  plane.  The  tubes  may  be  easily  bent 
when  heated  red-hot  at  the  proper  points  in  the  alcohol  or  gas  flame. 
See  that  the  four  pieces  are  bent  alike.  In  the  middle  of  the  cork, 
cut.  a  neat  hole  a  little  smaller  than  the  tube  first  prepared.  Near 
the  edge  of  the  cork,  at  equal  distances,  cut  four  holes  a  little 
smaller  than  the  four  pieces  of  bent  tubing.  Push  the  open  end  of 
the  straight  tube  through  the  middle  hole.  From  the  other  side  of 
the  cork,  enter  one  end  of  each  bent  tube  into  one  of  the  four  holes. 
Place  the  cork  with  its  five  tubes  into  the  end  of  the  chimney,  see- 
ing to  it  that  the  straight  tube  lies  along  the  axis  of  the  chimney, 
i.  e.,  that  it  is  parallel  with  the  sides  of  the  chimney.  The  closed  end 
of  the  central  tube  should  be  near  the  open  end  of  the  lamp-chimney. 
In  pushing  the  tubes  into  the  cork,  grasp  the  tube  (previously  dip- 
ped in  soap  and  water)  near  the  cork,  and  screw  it  in  with  a  slow, 
rotary,  onward  motion.  See  that  the  bent  tubes  are  at  right-angles  to 
each  other,  like  those  shown  in  Fig.  91.  For  a  support,  take  a  piece 
of  stout  wire,  small  enough  to  turn  easily  in  the  central  tube,  and,  a 


564  APPENDIX. 

little  longer  than  the  chimney.  Place  one  end  in  the  middle  of  a  tin 
pepper-box  and  fill  the  box  with  melted  lead.  This  makes  a  firm 
base.  File  the  other  end  of  the  wire  to  a  sharp  point.  For  a  few 
cents,  such  a  wire  with  an  iron  base  may  be  had  ready  made  at  the 
stationer's.  Pass  the  straight  tube  of  the  apparatus  over  this  wire 
until  the  closed  end  of  the  tube  rests  upon  the  sharpened  point.  The 
chimney,  with  its  four  horizontal  arms,  is  now  delicately  suspended, 
free  to  revolve  in  stable  equilibrium.  Place  the  apparatus  in  the 
middle  of  a  tub  and  pour  water  into  the  open  end  of  the  chimney. 
Tour  wheel  will  work  as  well  as  Queen's.  The  satisfaction  of  seeing 
the  machine  work  and  knowing  that  you  made  it  will  amply  repay 
the  cost,  leaving  the  instruction  and  added  skill  for  clear  profit. 

APPENDIX    G. 

Weight  of  Air.— (See  §  272.)  A  little  thought  concerning  the 
full  meaning  of  Archimedes'  Principle  will  show  that  if  a  body  weighs 
less  than  its  own  bulk  of  air  it  will  rise  in  the  air.  Thus,  soap- 
bubbles  filled  with  hydrogen  or  other  light  gas  will  ascend.  If  the 
bubble  be  made  from  hot  water  and  filled  with  warm  air  it  will 
rise ;  if  it  be  made  from  cold  water  and  filled  with  cold  air  it  will 
fall.  (Explain  why.)  The  same  principle  applies  to  balloons.  A 
balloon  will  support  a  weight  equal  to  the  difference  between  the  weight 
of  the  balloon  with  the  contained  gas  and  the  weight  of  the  air  dis- 
placed. A  liter  of  hydrogen  weighs  0.0896  g.  ;  a  liter  of  coal  gas, 
from  0.45  g.  to  0.85  g.  ;  a  liter  of  air  heated  to  200°  Centigrade,  about 
0.8  g.  On  June  5th,  1783,  at  Annonay,  about  40  miles  from  Lyons, 
France,  the  Montgolfier  Bros,  inflated  a  linen  globe  105  feet  in  diam- 
eter with  heated  air.  When  released,  it  rose  to  a  great  height  and 
descended  in  10  minutes  at  a  distance  of  1^  miles.  This  was  the  dis- 
covery of  the  balloon.  During  the  siege  of  Paris  in  1870,  the 
Parisians  communicated  with  the  outer  world  by  means  of  balloons 
about  50  feet  in  diameter,  having  a  capacity  of  about  70,600  cu.  ft. 
These  balloons,  with  net  and  car,  weighed  about  1,000  pounds  each 
and  had  a  carrying  ability  of  about  2,000  pounds.  Balloons  have 
been  made  about  100  feet  in  diameter,  having  a  capacity  of  about 
half  a  million  cubic  feet.  In  1861-,  an  ascent  was  made  to  a  height 
of  seven  miles. 

Air  in  motion  constitutes  a  wind  and  has  energy  by  virtue  of  its 
weight  and  velocity.  Winds  are  utilized  for  moving  ships,  for 
driving  windmills,  etc.  They  arise  from  atmospheric  disturbances 
caused  by  solar  heat.  The  energy  of  wind-power  like  that  of  water 
r>ower  (§8  260,  746)  is,  therefore,  traceable  to  the  sun  as  its  source. 


APPENDIX. 


565 


APPENDIX   H. 

Atmospheric  Pressure.— (See  §  275.)  Into  a  bent  glass 
tube,  ACS,  pour  mercury  to  a  height  of  about  20  inches,  or  50  cm. 
The  mercury  will,  of  course,  stand  at  exactly  the  same  level,  ac,  in 
the  two  branches.  If  equal  pressures  of  any  kind  be  exerted  upon 
the  surfaces  of  the  mercury  at  a  and  c,  this  level  will  not  be  dis- 
turbed, while  any  difference  of  pressure  would  be 
promptly  shown  by  the  movement  of  the  mercury 
and  a  consequent  difference  in  the  heights  of  the 
two  mercury  columns.  The  atmosphere  presses 
upon  both  mercurial  surfaces,  at  a  and  c,  but  it 
presses  upon  them  equally  and,  therefore,  does  not 
change  the  common  level.  Into  the  arm,  A,  push 
an  air-tight  piston,  p,  which  has  a  valve  opening 
upward  but  not  downward.  As  this  piston  is  pushed 
downward,  the  air  in  A  escapes  through  this  valve 
and  p  finally  rests  upon  the  surface  of  the  mercury 
at  a.  When  the  piston,  p,  is  subsequently  lifted  to 
A,  the  atmospheric  pressure  is  wholly  removed  from 
the  surface  of  the  mercury  in  that  arm  of  the  tube, 
while  it  acts  with  unchanged  intensity  upon  the  sur- 
face at  c.  The  consequence  is  that  the  mercury  fol- 
lows the  piston  until  there  is  a  difference  of  about 
760  mm.  or  30  inches  between  the  levels  of  the  mer- 
cury in  the  two  arms  of  the  tube.  If  the  tube  have 
a  sectional  area  of  one  square  inch,  the  mercury  thus 
supported  would  weigh  about  15  pounds,  and  would 
exactly  equal  the  weight  of  an  air  column  of  the 


FIG.  399. 


same  sectional  area,  reaching  from  the  apparatus  to  the  upper  sur- 
face of  the  atmosphere. 


APPENDIX   I. 

Copper  Wire. — Copper  wire  is  usually  designated  by  its 
gauge.  Unfortunately  there  are  several  gauges  in  common  use,  of 
which  the  most  important  two  are  the  English  or  Birmingham  wire 
gauge  (B.  W.  G.}  and  the  American  or  Brown  and  Sharpe  (B.  &  8.} 
gauge.  For  corresponding  numbers,  the  B.  W.  G.  is  a  little  larger 
than  the  B.  &  8.  The  following  table  of  some  of  the  more  common 
sizes  will  be  convenient  for  reference ; 


566 


APPENDIX. 


AMERICAN   WIRE    GAUGE  (B  &  S.). 


DIAMETER  IN 

DIAMETER  IN 

No. 

CIRCULAR 

OHMS 

PER 

No. 

CIRCULAR 

OHMS 

PER 

MILS, 

MILLIM 

MILS. 

1000  FT. 

MILS. 

MILLIM, 

MILS,      1000  B-T. 

.051 

19 

0000 

460.00 

11.684 

211600.0 

35.39 

.899 

1252.4 

8.617 

000 

409.64 

10.405      167805.0 

.064 

20 

31.96 

.812 

1021.5        10.566 

00 

364.80 

9.266      133079.4 

.081 

21 

28.46 

.723 

810.1        13.323 

0 

324.95 

8.254      105592.5 

.102 

22 

25.35 

.644 

642.7        16.799 

1 

289.30 

7.348       83694.2 

.129 

23 

22.57 

.573 

509.5        21.185 

«|  257.63 

6.544       66373.0 

.163 

|  24 

20.10 

.511 

404  0        26.713 

3 

229.42 

5.827       52634.0 

.205 

1  25 

17.90 

.455 

320.4        33.684 

4 

204.31 

5.189       41742.0 

.259 

26 

15.94 

.405 

254.0        42.477 

5 

181.94 

4.621       33102.0 

.326 

i  27 

14.19 

.361 

201.5        53.503 

6    162.02 

4.115       26250.5 

.411 

28 

12.64 

.321 

159.8        67.542 

7    144.28 

3.665       20816.0 

.519 

29 

11.26 

.286 

126.7 

85.170 

8    128.49 

3.264 

16509.0 

.654 

30 

10.03 

.255 

100.5 

107.391 

9    114.43 

2.907 

13094.0 

.824 

31 

8.93 

.227 

79.7 

135.402 

10    101.89 

2.588 

10381.0 

1.040 

32 

7.95 

.202 

63.2 

170.765 

11      90.74 

2.305 

8234.0        1.311 

33 

7.08 

.180 

50.1 

215.312 

12      80.81 

2.053 

6529.9        1.653 

34 

6.30 

.160 

39.7 

271.583 

13      71.96 

1.828 

5178.4 

2.084 

35 

5.61 

.143 

31.5 

342.443 

14     04.01 

1.628 

4106.8 

2.628 

36 

5.00 

.127 

25.0 

431.712 

15,     67.07 

1.450 

3256.7 

3.314 

37 

4.45 

.113 

19.8 

544.287 

161     50.83 

1.291 

2582.9 

4.179 

88 

3.96 

.101 

15.7 

686.511 

17j     45.26 

1.150 

2048.2 

5.269 

39 

3.53 

.090 

12.5 

865.046 

18      40.30 

1.024 

1624.3 

6.645 

40 

3.14 

.080 

9.9 

1091.865 

Note. — The  second  column  gives  the  diameters  in  thousandths  of  an  inch  ;  the 
third  column,  in  millimeters.  The  fourth  column  gives  the  equivalent  number  of 
wires  each  one  mil  in  diameter.  The  numbers  therein  given  are  the  squares  of  the 
diameters  in  mils.  By  multiplying  the  numbers  in  the  fifth  column  by  5.28,  the 
resistances  per  mile  may  be  found.  The  resistance  for  any  other  metal  than  cop- 
per may  be  found  by  multiplying  the  resistance  given  in  the  table  by  the  ratio 
between  the  specific  resistance  of  copper  and  the  specific  resistance  of  the  given 
metal.  (See  table  of  specific  resistances  in  Appendix  K  [2]).  The  resistances 
given  in  the  table  are  for  pure  copper  wire  at  a  temperature  of  75U  F.  or  24°  C. 
Ordinary  commercial  copper  wire  has  a  conductivity  of  about  95  or  96  per  cent. 
that  of  pure  copper.  Consequently,  the  resistances  of  such  wires  will  be  about  5 
per  cent,  greater  than  those  given  in  the  table. 

STUBS'   OR  BIRMINGHAM  WIRE  GAUGE  (B.  W.   G.). 


DlAl 

IETER  IN 

Wll 

DIAJ 

UETER  IN 

DIAJ 

IETER  IN 

MILS. 

MILLIM. 

MILS. 

MILLIM. 

MILS. 

MILLIM. 

too 

••><) 
1 

4 

6 

454 
380 
300 
238 
203 

11.53 
9.65 
7.62 
6.04 
5.16 

8 

is 

14 

16 

165 
134 
109 

OQ 

65 

4.19 
3.40 
2.77 
2.11 
1.65 

18 
20 
24 
30 
36 

49 
35 
22 
12 
4 

1.24 
0.89 
0.55 
0.81 
0.10 

The  catalogue  of  electrical  wires  (furnished  gratis  by  Holmes,  Booth  &  Haydens, 
22  Murray  street,  New  York  City,  or  by  The  Electrical  Supply  Co.,  17  Dey  street), 
contains  many  valuable  tables  and  other  information. 


APPENDIX.  567 


APPENDIX    J. 

The  Ijeycleii  «Jar. — The  following  is  extracted  (as  much  other 
information  in  this  volume  has  been)  from  Silvanus  Thompson's 
"  Elementarj  Lessons  in  Electricity  and  Magnetism": 

The  existence  of  a  residual  charge  (§  356)  can  be  explained  either 
on  the  supposition  that  the  dielectric  is  composed  of  heterogeneous 
particles  which  have  unequal  conducting  powers  or  on  the  hypothesis 
that  the  molecules  are  actually  subjected  to  a  strain  from  which, 
especially  if  the  stress  be  long  continued,  they  do  not  recover  all  at 
once.  There  is  an  analogy  between  this  phenomenon  and  that  of 
the  "  elastic  recovery  "  of  solid  bodies  after  being  subjected  to  a  bend- 
ing or  a  twisting  strain.  A  fibre  of  glass,  for  example,  twisted  by  a 
certain  force,  flies  back  when  released  to  almost  its  original  position, 
a  slight  sub-permanent  set  remains  from  which,  however,  it  slowly 
recovers  itself,  the  rate  of  its  recovery  depending  on  the  amount  and 
duration  of  the  original  twisting  strain.  It  is  possible  to  superpose 
several  residual  charges,  even  charges  of  opposite  signs,  which 
apparently  "  soak  out "  as  the  strained  material  gradually  recovers 
itself. 

As  to  the  precise  nature  of  the  molecular  or  mechanical  operations 
in  the  dielectric  when  thus  subjected  to  the  stress  of  electrostatic 
induction,  nothing  is  known.  One  pregnant  experiment  of  Faraday 
is  of  great  importance,  by  showing  that  induction  is,  as  he  expressed 
it,  "an  action  of  contiguous  particles."  In  a  glass  trough,  T (Fig. 
400),  is  placed  some  oil 
of  turpentine,  in  which 

are  put  some  fibres  of  dry       T~~~**fij7^  jj 

silk  cut  into  small  bits. 
Two  wires  pass  into  the 
liquid,  one  of  which  is 
joined  to  earth,  the  other 

being  put  into  connection  with  0,  the  prime  conductor  of  an  elec- 
trical machine.  The  bits  of  silk  come  from  all  parts  of  the  liquid  and 
.form  a  chain  of  particles  from  wire  to  wire,  p  to  p'.  On  touching 
them  with  a  glass  rod  they  resist  being  pushed  aside,  though  they 
at  once  disperse  if  the  supply  of  electricity  is  stopped.  Faraday 
regarded  this  as  typical  of  the  internal  actions  in  every  case  of  in- 
duction across  a  dielectric,  the  particles  of  which  he  supposed  to  be 
41  polarized,"  that  is,  to  be  turned  into  definite  positions,  each  particle 
having  a  positive  and  a  negative  end.  The  student  will  perceive  an 
obvious  analogy,  therefore,  between  the  condition  of  the  particles  of 


568 


APPENDIX. 


a  dielectric  across  which  electrostatic  induction  is  taking  place,  and 
the  molecules  of  a  piece  of  iron  or  steel  when  subjected  to  magnetic 
induction. 

Siemens  has  shown  that  the  glass  of  a  Leyden  jar  is  sensibly 
warmed  after  being  several  times  rapidly  charged  arid  discharged. 
This  obviously  implies  that  molecular  movement  accompanies  the 
changes  of  dielectric  stress. 

The  internal  volume  of  a  Leyden  jar  is  increased  when  it  is 
charged,  as  though  the  attraction  between  the  two  charged  surfaces 
compressed  the  glass  and  caused  it  to  expand  laterally. 


APPENDIX   K. 

(1.)  Electrical  Resistance. — The  idea  implied  in  resistance 
is  that  of  a  force  opposing  the  E.  M.  F.  which  maintains  the  current. 
It  is  analogous  to  friction  in  mechanics.  The  resistances  of  a  circuit 
are  of  two  kinds,  viz.,  the  resistances  of  the  conductors  themselves 
and  the  resistances  due  to  imperfect  contact.  The  latter  kind  is 
affected  by  pressure,  which  brings  the  surfaces  into  more  intimate 
contact.  The  contact  resistance  of  two  wire  conductors  may  vary 
from  infinity  to  the  small  fraction  of  an  ohm.  Hence,  great  care 
should  be  exercised  in  splicing  two  such  wires,  by  seeing  that  the 
contact  surfaces  are  clean  and  that  the  wires  are  tightly  twisted  to- 
gether. In  many  cases,  it  is  desirable  to  solder  the  spliced  wires. 

(2.)  Specific  Resistance.—  The  specific  resistance  of  a  sub- 
stance is  best  stated  as  the  resistance  in  absolute  units  (i.  e.,  in 
billionths  of  an  ohm)  of  a  cubic  centimeter  of  the  substance. 

TABLE  OF  SPECIFIC  EESI8TANCES  AND  KELATIVE  CONDUCTIVITIES. 


SUBSTANCE. 

SPECIFIC  RESISTANCE. 

RELATIVE  CONDUCTIVITY. 

Metals. 
Silver, 

gsr 

Platinum, 
Iron  (soft), 
Lead, 
German  Silver, 
Mercury  (liquid). 
Selenium  (annealed), 

1,609 
1,642 
2,154 
8,939 
9,827 
19,847 
21,170 
96,146 
6  x   101S 

100             ;.- 

98 
74 
18 
16 
8 
7'5 
1-6 

47To66  OOO"O(>5 

Lif/ttifiK. 
Pure  Water  at  22°  C. 
Dilute  Sulphuric  Acid  ) 
(ft  acid),  •                f 
Dilute  HaSO«  (;  acid) 

7-18    x  1010 
•332  x  101" 
•126  x  10'  ° 

Less  than  one  millionth 
part. 

Insulators. 
Glass  (at  200°  C), 
Gutta-percha  (at  20"  C) 

2-27    x  1018 
8'5      x  1023 

Less  than  one  millionth 
of  a  millionth  part. 

APPENDIX.  569 

If  the  poles  of  100  Daniell  cells  be  connected  with  tin-foil  sheets 
1  m.  square  pasted  on  opposite  faces  of  a  plate  of  gutta-percha  1  cm. 
thick,  less  than  10  coulombs  would  pass  through  this  circuit  of  very 
high  resistance  in  a  whole  century. 

Those  substances  that  possess  a  high  conducting  power  for  elec- 
tricity are  the  best  conductors  of  heat  (§  604  [6.]).  Liquids  are  worse 
conductors  than  the  metals  and  gases  are  perfect  non-conductors, 
3xcept  when  so  rarefied  as  to  admit  of  discharge  by  convection 
through  them. 

(3.)  Effects  of  Heat  on  Resistance. — The  resistance  of  a 
conductor  is  constant  as  long  as  the  molecular  condition  of  the  con- 
ductor is  unchanged.  But  it  is  changed  by  heat,  strain,  tempering, 
magnetization  and,  in  some  cases,  by  light.  The  resistance  of  metals 
increases  considerably  as  the  temperature  is  raised.  On  the  other 
hand,  the  resistance  of  carbon  appears  to  diminish  on  heating. 
German- silver  and  other  alloys  do  not  show  so  much  change,  hence 
they  are  used  in  making  standard  resistance-coils.  Liquids  that 
conduct  only  by  being  electrolyzed  conduct  better  as  the  tempera- 
ture rises.  Vide,  Encyclopaedia  Britannica,  vol.  viii,  p.  52  (Ninth 
edition}. 

(4.)  Effect  of  Light  on  Resistance.— Ordinary  fused  or 
vitreous  selenium  (Chemistry,  §  160)  is  a  very  bad  conductor ;  its 
resistance  being  nearly  3.8xl010  times  as  great  as  that  of  copper. 
When  carefully  annealed  (by  keeping  for  some  hours  at  a  tempera- 
ture of  about  220°  C.,  just  below  its  fusing  point,  and  subsequently 
cooling  slowly),  it  assumes  a  crystalline  condition,  in  which  its  electric 
resistance  is  considerably  reduced.  In  the  latter  condition,  especially, 
its  resistance  is  considerably  and  instantly  lessened  by  exposure  to 
light.  Greenish-yellow  rays  are  the  most  effective.  Prof.  Graham 
Bell  and  Mr.  Sumner  Tainter  have  devised  forms  of  "  selenium  cells," 
in  which  the  selenium  is  formed  into  narrow  strips  between  the 
edges  of  broad  conducting  plates  of  brass,  thus  securing  both  a  re- 
duction of  the  transverse  resistance  and  a  large  amount  of  surface- 
exposure  to  light.  The  resistance  of  such  a  cell  in  the  dark  was 
300  ohms;  when  exposed  to  sunlight,  it  had  a  resistance  of  but  150 
ohms.  This  property  of  selenium  has  been  applied  in  the  construc- 
tion of  the  Photophone,  an  instrument  which  transmits  sounds  to  a 
distance  by  means  of  a  beam  of  light.  The  light  is  reflected  to  the  dis- 
tant station  by  a  thin  mirror  thrown  into  vibrations  by  the  voice  ;  the 
beam  falling,  consequently,  with  varying  intensity  upon  a  receiver  of 
selenium  connected  in  circuit  with  a  small  battery  and  a  Bell  telephone. 
The  sounds  are  thus  reproduced  by  the  variations  of  the  current, 


570 


APPENDIX. 


Similar  properties  are  possessed,  to  a  smaller  degree,  by  tellurium 
(Chemistry,  §  161). 

APPENDIX    L. 

(1.)  The  Tangent  Galvanometer.— it  is  not  possible  to 
make  a  galvanometer  in  which  the  strength  of  current  shall  be  pro- 
portional to  the  angle  of  deflection  through  its  whole  range.  But  a 
simple  galvanometer  may  be  made  in  which  the  strength  of  the 
current  shall  be  proportional  to  the  tangent  of  the  angle  of  deflec- 
tion. The  tangent  gal- 
vanometer, one  form  of 
which  is  shown  in  Fig. 
401,  is  such  an  instrument. 
A  horizontal  needle  (§  439a) 
not  more  than  an  inch 
long  is  delicately  suspend- 
ed at  the  centre  of  a  stout 
copper  wire  hoop  about 
fifteen  inches  in  diameter. 
The  single  coil  or  hoop 
being  placed  in  the  mag- 
netic meridian,  a  current 
flowing  through  the  coil  will 
deflect  the  needle  through 
such  an  angle  that  the 
tangent  of  the  angle  of 
deflection  is  proportional  to 
the  strength  of  the  current. 
For  example,  suppose  that 

a  certain  battery  gives  a  deflection  of  15°  and  a  second  battery  gives 
a  deflection  of  30°.  The  numbers  of  amperes  are  not  in  the  ratio  of 
15  : 30  but  in  the  ratio  of  tan  15°  :  tan  30°.  The  values  of  such 
tangents  must  be  obtained  from  a  Table  of  Natural  Tangents  (see 
below),  from  which  it  will  be  found  that  the  strengths  of  the  currents 
are  in  the  ratio  of 

0.268  :  0.577,  or  about  10  :  22. 

If  a  known  current,  (7,  gives  a  deflection  of  m  degrees  and  an 
unknown  current,  c,  gives  a  deflection  of  n  degrees,  the  value  of  c 
may  be  found  (with  the  help  of  the  table  below)  from  the  proportion 
C  :  c  ::  tan  m  :  tan  n. 

A  delicate,  stiff  pointer  or  index  of  aluminum  (Chemistry,  §  346) 
Is  usually  fastened  to  the  short,  stout  needle  of  the  tangent  gal- 
vanometer. But,  at  the  best,  this  instrument  is  not  very  sensitive. 


APPENDIX. 


571 


TABLE  OF  NATURAL  TANGENTS. 


ABC. 

TANGENT. 

ABC. 

TANGENT. 

ABC. 

TANGENT. 

ABC. 

TANGENT. 

1° 

.017 

24° 

.445 

47° 

1.07 

70° 

2.75 

2 

.035 

25 

.466 

48 

1.11 

71 

2.90 

3 

.052 

26 

.488 

49 

1.15 

72 

3.08 

4 

.070 

27 

.510 

50 

1.19 

73 

3.27 

5 

.087 

28 

.532 

51 

1.23 

74 

3.49 

6 

.105 

29 

.554 

52 

1.28 

75 

3.73 

7 

.123 

30 

.577 

53 

1.33 

76 

4.01 

8 

.141 

31 

.601 

54 

1.38 

77 

4.33 

9 

.158 

32 

.625 

55 

1.43 

78 

4.70 

10 

.176 

33 

.649 

56 

1.48 

79 

5.14 

11 

.194 

3t 

.675 

57 

1.54 

80 

5.67 

12 

.213 

35 

.700 

58 

1.60 

81 

6.31 

13 

.231 

36 

.727 

59 

1.66 

82 

7.12 

14 

,249 

37 

.754 

60 

1.73 

83 

8.14 

15 

.268 

38 

.781 

61 

1.80 

84 

9.51 

16 

.287 

39 

.810 

62 

1.88 

85 

11.43 

17 

.306 

40 

.839 

63 

1.96 

86 

14.30 

18 

.325 

41 

.869 

64 

2.05 

87 

19.08 

19 

.344 

42 

.900 

65 

2.14 

88 

28.64 

20 

.364 

43 

.933 

66 

2.25 

89 

57.29 

21 

.384 

44 

.966 

67 

2.36 

90 

Infinite. 

22 

.404 

45 

1.000 

68 

2.48 

23 

.424 

46 

1.036 

69 

2.61 

(2.)  The  Sine  Galvanometer. — Any  sensitive  galvanometer, 
the  needle  of  which  is  directed  by  the  earth's  magnetism  and  in 
which  the  frame  on  which  the  coils  are  wound  is  capable  of  being 
turned  round  a  central  axis,  may  be  used  as  a  Sine  Galvanometer. 
The  coils  are  set  parallel  to  the  needle  (i.  e.,  in  the  magnetic  merid- 
ian). The  current  is  then  sent  through  the  coils,  deflecting  the 
needle.  The  coil  is  then  turned  until  it  overtakes  the  needle  which 
once  more  lies  parallel  to  the  coil.  Two  forces  are  now  acting  on 
xhe  needle  and  balancing  each  other,  viz.,  the  directive  force  of  the 
earth's  magnetism  and  the  deflecting  force  of  the  current  flowing 
through  the  coil.  At  this  moment,  the  strength  of  the  current  is  pro- 
portional to  the '  sine  of  the  angle  through  which  the  coil  has  been 
turned.  The  values  of  the  sines  must  be  obtained  from  a  Table  of 
Natural  Sines. 

TABLE    OP   NATURAL    SINES. 


ABC. 

SINE. 

ABC. 

SINE. 

ABC. 

SINE. 

ABC. 

SINE. 

0° 

.000 

9° 

.156 

50U 

.766 

83° 

998 

1 

.017 

10 

.174 

55 

.819 

84 

995 

2 

.035 

15 

.259 

60 

.866 

85 

996 

3 

.052 

20 

.342 

65 

.906 

86 

998 

4 

.070 

25 

.423 

70 

.940 

87 

999 

5 

087 

30 

.500 

75- 

.966 

88 

999 

6 

1 

.105 
.122 
.139 

35 
40 
45 

.574 
.643 
.707 

80 
81 
82 

.985 
.988 
.990 

89 
90 

999 
1000 

572 


APPENDIX. 


(3.)  The  Mirror  Galvanometer.— In  this  instrument,  a 
very  light  mirror  of  silvered  glass  is  fastened  to  the  needle  so  that  a 
ueam  of  light  may  be  reflected  upon  a  graduated  scale.  The 
slightest  motion  of  the  needle  is  thus  magnified  and  made  apparent. 
Fig.  402  shows  the  mirror  galvanometer  devised  by  Sir  W.  Thomson 


FIG.  402. 

for  signalling  through  submarine  cables.  The  magnet  consists  of 
one  or  more  pieces  of  steel  watch  spring  fastened  to  the  back  of  a 
small  concave  mirror  which  is  hung  by  a  single  fibre  of  cocoon  silk 
within  the  coil.  A  curved  magnet,  carried  on  a  vertical  support 
above  the  coil,  serves  to  counteract  the  earth's  magnetism  and  to 
direct  the  needle  within  the  coil.  A  beam  of  light  from  the  lamp 
passes  through  a  small  opening  under  the  scale,  falls  upon  the 
mirror  and  is  reflected  back  upon  the  scale.  The  curved  magnet 
above  the  coil  enables  the  operator  to  bring  the  spot  of  reflected 
light  to  the  zero  mark  at  the  middle  of  the  scale.  A  current  passing 
through  the  coil  turns  the  needle  and  its  mirror,  thus  shifting  the 
spot  of  light  to  the  right  or  left  of  the  zero  point.  The  apparatus  i? 
wondrously  sensitive.  The  current  produced  by  dipping  the  point 
of  a  brass  pin  and  the  point  of  a  steel  needle  into  a  drop  of  salt  water 
and  closing  the  external  circuit  through  this  instrument  sends  the 
spot  of  light  swinging  way  across  the  scale. 

(4.)  The  Differential  Galvanometer,— In  this  instm 


APPENDIX. 


573 


ment,  the  coil  is  made  of  two  separate  wires  wound  side  by  side. 
If  two  equal  currents  are  sent  through  these  wires  in  opposite 
directions,  the  needle  will  not  be  deflected.  If  the  currents  are 
unequal,  the  needle  will  be  deflected  by  the  stronger  one  with  a 
force  corresponding  to  the  difference  of  the  strengths  of  the  two 
currents.  It  is  much  used  in  "nil"  methods  of  measurements. 
[See  App.  M  (3).J 

APPENDIX    M. 

Electrical  Measurements. — The  wonderful  advance  made 
by  electrical  science  within  the  last  few  years  is  largely  due  to  the 
adoption  of  a  system  of  exact  measurements.  In  September,  1881, 
the  Paris  Electrical  Congress,  composed  of  representative  electricians 
of  all  countries,  established  a  system  of  new  (C.  G.  S.)  electrical  units 
which  are  now  generally  accepted  and  used. 

(1.)  Resistance  Coils. — Wires  of  standard  resistance  are  now 
sold  by  instrument  makers  under  the  name  of  Resistance  Coils. 
They  consist  of  coils  of  german- 
silver  (or  sometimes  silver-iridium 
alloy),  wound  with  great  care  and 
adjusted  to  such  a  length  as  to 
have  resistances  of  a  definite  num- 
ber of  ohms.  In  order  to  avoid 
self-induction  and  the  consequent 
sparks  at  the  opening  or  closing  of 
the  circuit,  they  are  wound  in  the 
peculiar  manner  indicated  in  Fig. 
403,  each  wire  (covered  with  silk  or 

paraffined- cotton)  being  doubled  on  itself  before  being  coiled  up.  Each 
end  of  a  coil  is  soldered  to  a  solid  brass  piece,  as  coil  1  to  A  and  B, 
coil  2  to  B  and  C;  the  brass  pieces  being  themselves  fixed  to  a  block 

of  ebonite  (forming 
the  top  of  the  "  resist- 
ance box  "),  with  suf- 
ficient room  between 
them  to  admit  of  the 
insertion  of  stout, 
well-fitting  plugs  of 
brass.  Fig.  404  shows 
a  complete  resistance- 
box,  as  fitted  up  for 
electrical  testing, 
FIG.  404.  with  the  plugs  in 


FIG.  403. 


574  APPENDIX. 

their  places.  So  long  as  the  plugs  remain  in,  the  current  flows 
through  the  solid  brass  pieces  and  plugs  without  encountering  any 
serious  resistance  ;  but  when  any  plug  is  removed,  the  current  can 
pass  from  the  one  brass  piece  to  the  other  only  by  traversing  the 
coil  thus  thrown  into  circuit.  The  series  of  coils  chosen  is  usually 
of  the  following  numbers  of  ohms'  resistance— 1,  2,  2,  5  ;  10,  20,  20*, 

50  ;  100,  200,  200,  500  ; up  to  10,000  ohms.    By  pulling 

out  one  plug  any  one  of  these  can  be  thrown  into  the  circuit  and 
any  desired  whole  number,  up  to  20,000,  can  be  made  up  by  pulling 
out  more  plugs ;  thus  a  resistance  of  263  ohms  will  be  made  up  as 
200  +  50  +  10  +  2  +  1. 

(2.)  Measuring-  External  Resistances. — (a.)  Suppose  that 

we  have  a  standard  battery  of  a  few 
Daniell's  cells,  joined  up  in  circuit 
with  R,  a  wire  of  unknown  resist- 
ance, and  with  a  galvanometer,  that 
indicates  a  current  of  a  certain 
strength,  as  shown  in  Fig.  405.  If 
we  remove  the  wire,  R,  and,  in  its 
place  in  the  circuit,  substitute  wires 
FIG.  405.  whose  resistances  we  know,  we  may, 

by  trying,   find  one   which,    when 

interposed  in  the  path  of  the  current,  gives  the  same  deflection  of 
t.ie  galvanometer  needle.  Hence,  we  shall  know  that  this  wire  and 
the  one  we  called  R  offer  equal  resistances  to  the  current. 

(6.)  A  rheostat  is  a  long  thin  wire  coiled  upon  a  wooden  cylinder, 
so  that  any  desired  length  of  the  wire  may  be  thrown  into  the 
circuit  by  unwinding  the  proper  number  of  turns  of  wire  off  the 
cylinder,  or  by  making  contact  at  a  point  at  any  desired  distance 
from  the  end  of  the  wire.  The  rheostat  has  been  superseded  by  the 
resistance  coils  mentioned  above. 

(c.)  The  method  explained  above  may  be  used  with  any  galva- 
nometer of  sufficient  sensitiveness,  but  if  a  tangent  galvanometer  is 
available  the  process  may  be  shortened.  Suppose  the  tangent 
galvanometer  and  an  unknown  resistance,  R,  to  be  included  in  the 
circuit,  as  in  Fig.  405,  and  that  the  current  is  strong  enough  to  pro- 
duce a  deflection  of  a  degrees.  Substitute  for  R  any  known 
resistance,  r,  which  will  alter  the  deflection  to  b  degrees  ;  then 
(provided  the  other  resistances  of  the  circuit  be  negligibly  small)  it 
is  clear  that  since  the  strengths  of  the  currents  are  proportional  to 
tan  a  and  tan  b  respectively,  the  resistance,  R,  may  be  calculated  by 
the  inverse  proportion : 

tan  a  :  tan  b  =  r  :  R. 


APPENDIX. 


575 


(d.)  With  a  differential  galvanometer  and  a  set  of  standard  resist- 
ance coils,  it  is  easy  to  measure  the  resistance  of  a  conductor.  Let 
the  circuit  of  a  battery  divide  into  two  branches,  so  that  part  of  the 
current  flows  through  the  given  resistance  and  round  one  set  of  coils 
of  the  galvanometer,  the  other  part  of  the  current  being  made  to  flow 
through  known  resistances  and  then  round  the  other  set  of  coils  in 
the  opposing  direction.  When  we  have  succeeded  in  matching  the 
imknown  resistance  by  one  equal  to  it  from  the  known  resistances, 
the  currents  in  the  two  branches  will  be  equal  and  the  needle  of  the 
differential  galvanometer  will  show  no  deflection.  With  an  accurate 
instrument,  this  method  is  very  reliable. 

Or  we  may  vary  the  resistance  of  the  second  circuit  until  it  balances 
the  given  resistance ;  remove  the  given  resistance  and  put  known 
resistances  in  its  place  until  the  galvanometer  again  shows  no  deflec- 
tion. This  is  the  better  way,  as  it  gives  good  results  even  if  the  two 
coils  of  the  galvanometer  are  not  exactly  symmetrical.  (Compare 
§  177.) 


FIG.  406. 

(e.)  The  best  of  all  the  ways  of  measuring  resistances  is,  however, 
with  a  set  of  standard  resistance  coils  and  the  important  instrument 
known  as  Wheatstone's  Bridge.  This  instrument  is  represented  by 
the  diagram  shown  in  Fig.  406.  The  circuit  of  a  constant  battery 
is  made  to  branch  at  P  into  two  parts  which  reunite  at  Q,  so  that 
part  of  the  current  flows  through  the  point  M,  the  other  through  the 
point  N.  The  four  conductors,  A,  B,  C  and  D,  are  called  the  arms 
of  the  bridge.  The  resistance  of  any  three  of  these  arms  being 
known,  that  of  the  remaining  one  may  be  calculated.  When  the 
current  that  starts  from  the  battery  arrives  at  P,  the  potential  will 
have  fallen  to  a  certain  value.  The  potential  of  the  current  in  the 


576 


APPENDIX. 


upper  branch  falls  again  to  M  and  continues  to  fall  to  Q.  The  po- 
tential of  the  lower  branch  falls  to  JV  and  continues  to  fall  until,  at 
<2,  it  is  of  the  same  value  as  that  of  the  upper  branch  at  the  same 
point.  If  the  ratio  of  the  resistance  of  G  to  the  resistance  of  D  is 
the  same  as  the  ratio  of  the  resistance  of  A  to  the  resistance  of  B, 
then  will  M  and  N  be  at  equal  potentials.  If  a  sensitive  galvanom- 
eter, placed  in  the  branch  wire  between  M  and  N,  shows  no  deflec- 
tion, we  may  know  that  M  and  JVare  at  equal  potentials  and  that 
the  resistances  of  the  four  arms  "balance"  by  being  in  proportion, 
thus : 

A:C  =  B:D. 

For  example,  if  the  resistances,  A  and  G,  are  (as  indicated  in  Fig. 
407)  10  ohms  and  100  ohms  respectively  and  the  resistance  of  G  is  15 
ohms,  the  resistance  of  D  will  be  150  ohms. 


FIG.  407. 

It  is  usual  to  construct  Wheatstone's  bridges  with  some  resistance 
coils  in  the  arms,  A  and  C,  as  well  as  with  a  complete  set  in  the 
arm,  B.  The  advantage  of  this  arrangement  is  that  by  adjusting  A 
and  G  we  determine  the  ratio  between  the  resistances  of  B  and  D 
and  can,  in  certain  cases,  measure  to  fractions  of  an  ohm.  Fig.  407 
shows  a  more  complete  scheme,  in  which  resistances  of  10,  100  and 
1,000  ohms  are  included  in  the  arms,  A  and  C. 

For  example,  suppose  that  we  have  a  wire,  the  resistance  of  which 
we  know  to  be  between  46  and  47  ohms  and  wish  to  measure  the 
fraction  of  an  ohm.  Insert  the  wire  at  D.  Make  the  resistance  of  A, 
100  ohms  and  that  of  C,  10  ohms.  In  this  case,  D  must  be  balanced 


APPENDIX.  577 

by  a  resistance  in  B,  10  times  as  great  as  that  of  D.  If,  on  trial, 
this  is  found  to  be  464  ohms,  we  know  that  the  resistance  of  D  is 
(464  x  10  -*- 100  =)  46.4  ohms. 

In  practice,  the  bridge  is  not  made  in  the  diamond  shape  of  the 
diagrams.  The  resistance  box  shown  in  Fig.  404  is  a  complete 
bridge,  the  appropriate  connections  being  made  by  screws  at  various 
points.  In  using  the  bridge,  the  battery  circuit  should  always  be 
made  by  depressing  the  key,  k,  before  K,  the  key  of  the  galvanometer 
branch  is  depressed.  This  avoids  the  sudden  "  throw" of  the  galva- 
nometer needle,  in  consequence  of  the  self-induction,  when  the  cir- 
cuit is  closed  (§  458). 

Vide,  Encyclopaedia  Britannica  (9th  edition),  vol.  viii,  pp.  43  to  46. 

(3.)  Measuring  Internal  Resistance.—  The  best  way  of 
determining  the  internal  resistance  of  a  voltaic  cell  is  to  join  two 
similar  cells  in  opposition  to  one  another,  so  that  they  send  no  cur- 
rent of  their  own.  Then  measure  their  united  resistance  (as  if  it 
were  the  resistance  of  a  wire)  as  just  described.  The  resistance  of 
one  cell  will  be  half  that  of  the  two. 

(4.)  Measuring-  Electromotive  Forces.  — The  usual 
method  of  measuring  E.  M.  F.  is  by  comparison  with  the  E.  M.  F. 
of  a  Daniell  cell  (=  1.079  volts). 

(a.)  Represent  the  E.  M.  F.  of  the  standard  cell  or  battery  by  E 
and  that  of  the  given  cell  or  battery  by  X.  Join  cell  X  with  the 
galvanometer  and  note  the  number  of  degrees  of  deflection  that  it 
produces  through  the  resistances  of  the  circuit.  Represent  this  de- 
flection by  a.  Then  add  enough  resistance,  R,  to  bring  the  deflec- 
tion down  to  b  degrees  (c.  g. ,  10  degrees  less  than  before).  Then 
substitute  the  standard  for  the  given  battery  in  the  circuit  and  adjust 
the  resistances  of  the  circuit  until  the  galvanometer  shows  a  deflec- 
tion of  a  degrees,  as  at  first.  Add  enough  resistance,  r,  to  bring  the 
deflection  down  to  b  degrees  as  before.  E,  R  and  r  being  known, 
X  may  be  found  from  the  proportion, 

r:R::E:  X, 

because  the  resistances  that  will  produce  an  equal  reduction  of  cur- 
rent will  be  proportional  to  the  electromotive  forces. 

(&.)  If  the  poles  of  a  standard  battery  are  joined  by  a  long,  thin 
wire,  the  potential  will  fall  uniformly  from  the  +  to  the  —  pole. 
Hence,  by  making  contacts  at  one  pole  and  at  a  point  any  desired 
distance  along  the  wire,  any  desired  proportional  part  of  the  whole 
electromotive  force  may  be  taken.  This  proportional  part  may  be 


578  APPENDIX. 

balanced  against  the  electromotive  force  of  any  other  battery,  or 
used  to  compare  the  difference  between  the  electromotive  forces  of 
two  different  cells. 

(c.)  A  galvanometer  having  a  coil  resistance  of  several  thousand 
ohms  (in  comparison  with  which  the  internal  resistance  of  a  battery 
or  dynamo  is  insignificant)  may  be  used  to  measure  E.  M.  F.,  for,  by 
Ohm's  law,  the  strength  of  current  that  such  a  battery  or  dynamo 
can  send  through  it  will  depend  only  on  the  E.  M.  F.  (or  difference 
of  potential)  between  the  ends  of  the  coil.  Such  a  galvanometer, 
properly  graduated,  is  called  a  voltmeter  or  a  potential  galvanometer. 
It  may  be  used  to  determine  the  difference  of  potential  between  any 
two  points  of  a  circuit  by  placing  the  galvanometer  in  a  shunt  circuit 
between  those  two  points. 

(d.)  The  following  method  was  devised  by  Dr.  C.  F.  Brush  for 
determining  the  difference  of  potential  between  the  terminals  of  a 
standard  Brush  arc  lamp  :  A  battery  of  48  small  Daniell  cells  had  its 
+  electrode  connected  to  the  +  terminal  of  the  lamp  (which  was  in 
the  dynamo  circuit)  and  its  —  electrode  connected  to  the  —  terminal 
of  the  lamp,  a  very  sensitive  galvanometer  being  placed  in  the  bat- 
tery circuit  which  was  thus  completed  through  the  lamp.  It  is  evi- 
dent that  if  the  difference  of  potential  between  the  ends  of  the  bat- 
tery is  greater  than  that  between  the  terminals  of  the  lamp,  the 
current  will  circulate  in  its  normal  direction  through  the  battery 
and  will  be  indicated  by  the  galvanometer;  but  if  this  potential  is 
less  than  that  of  the  lamp,  the  current  will  flow  through  the  battery 
but  in  a  reverse  direction  and  will  be  so  indicated  by  the  galvanom- 
eter; while,  if  the  difference  of  potential  is  the  same  in  both,  no 
current  will  pass  in  either  direction  through  the  battery  and  the 
galvanometer  will  show  no  deflection. 

The  E.  M.  F.  of  the  battery  exceeding  the  difference  of  potential 
between  the  terminals  of  the  lamp,  cells  were  gradually  removed 
until  the  galvanometer  indicated  no  current  or  currents  fluctuating 
from  zero  equally  in  both  directions.  The  large  number  of  observa- 
tions made  sufficiently  eliminated  the  error  due  to  the  fact  that  no 
fraction  of  a  single  cell  of  the  battery  could  be  used  in  the  experi- 
ments. This  method  of  measuring  the  difference  of  potential  be- 
tween the  terminals  of  the  lamp  proved  to  be  extremely  satisfactory 
and  certain  in  its  operation,  the  addition  or  subtraction  of  a  single 
cell  of  battery  being  sufficient  to  deflect  the  galvanometer  needle 
strongly  to  the  right  or  left,  By  finding  the  average  result  of  all 
the  observations,  it  was  found  that  the  difference  of  potential  be- 
tween the  terminals  of  the  average  lamp  was  equal  to  that  of  42.46 
cells  of  the  battery,  or  45.8  volts. 


APPENDIX.  579 

The  resistance  of  the  lamp  being  measured  was  found  to  be  4.56 
ohms.  Therefore,  the  current  passing  in  the  dynamo  circuit  was 
(45.8  -T-  4.56  =)  10.04  amperes. 

(5.)  Measuring  Capacity.— The  capacity  of  a  condenser  is 
generally  measured  by  comparing  it  with  the  capacity  of  a  standard 
condenser.  Fig.  408  represents  a  ^  micro- 
farad condenser.  The  two  brass  pieces 
upon  the  ebonite  top  are  connected  respect- 
ively with  the  two  series  of  alternate  sheets 
of  tin-foil.  The  plug  between  them  serves 
to  keep  the  condenser  discharged  v.-hen  not 
in  use. 

(a.)  Charge  the  given  condenser  to  a  cer- 
tain potential  and  make  it  share  its  charge  Fir  T  8 
with  a  condenser  of  known  capacity. 
Measure  the  potential  to  which  the  charge  sinks.  Calculate  the 
original  capacity,  which  will  bear  the  same  ratio  to  the  total  capacity 
of  the  two  condensers  that  the  final  potential  bears  to  the  original 
l>otential. 

(6.)  Charge  the  two  condensers  simultaneously  from  one  pole  of 
the  same  battery,  interposing  high  resistances  in  each  branch  and 
adjusted  so  that  the  potential  rises  at  an  equal  rate  in  both ;  then 
the  capacities  are  inversely  proportional  to  the  resistances  through 
which  they  are  respectively  being  charged. 

(c.)  The  following  method  requires  no  condenser  :  Allow  the 
given  condenser  to  discharge  itself  slowly  through  a  wire  of  very 
high  resistance.  The  time  taken  for  the  potential  to  fall  to  any 
given  fraction  of  its  original  value  is  proportional  to  the  resistance, 
to  the  capacity  and  to  the  logarithm  of  the  given  fraction. 

(d.)  The  capacity  of  a  condenser,  like  that  of  a  simple  conductor, 
is  measured  by  the  quantity  of  electricity  required  to  produce  unit 
rise  of  potential. 

APPENDIX  N. 

Field  of  Force.—"  A  field  of  force  is  a  region  such  that  a 
paiticle  constituting  a  part  of  a  mutually  interacting  system,  placed 
at  any  point  in  the  region,  will  be  acted  on  by  a  force  and  will  move, 
if  free  to  do  so,  in  the  direction  of  the  force.  The  particle  so  mov- 
ing would,  if  it  had  no  inertia,  describe  what  ifl  called  a  line  of 
force,  the  tangent  to  which,  at  any  point,  is  the  direction  of  the 
force  at  that  point.  The  strength  of  the  field  at  a  point  is  measured 
by  the  force  developed  by  unit  quantity  at  that  point  and  is  ex- 


580  APPENDIX. 

pressible,  in  terms  of  lines  of  force,  by  the  convention  that  each  line 
represents  a  unit  of  force  and  that  the  force  acting  on  unit  quantity 
at  any  point  varies  as  the  number  of  lines  of  force  which  pass  per- 
pendicularly through  unit  area  at  that  point.  Each  line,  therefore, 
represents  the  direction  of  the  force  and  the  number  of  lines  in  unit 
area,  the  strength  of  field.  An  assemblage  of  such  lines  of  force, 
considered  with  reference  to  their  bounding-surface,  is  called  a  tube 
of  force," — Anthony  and  Brackett. 

APPENDIX    0. 

The  Telephone .  —(See  §  506.)  The  theory  that  the  diaphragm 
of  the  receiving  telephone  is  made  to  vibrate  to  and  fro  hy  the  vary- 
ing intensity  of  the  magnetic  attraction  of  the  iron  core  has  lately 
been  questioned.  Many  experiments  go  to  show  that  the  variations 
in  the  magnetic  intensity  of  the  iron  core  are  too  feeble  to  produce 
such  mechanical  effects.  It  also  appears  that  paper  and  other  sub- 
stances may  replace  the  iron  of  the  diaphragm  in  the  receiving  tele- 
phone, without  destroying  the  sounds,  and  that  the  diaphragm  may 
even  be  removed  and  the  sounds  still  produced  and  transmitted  to 
the  ear.  These  facts  are  believed  to  show  that  the  reproduced  sound 
is  due  to  movements  of  the  molecules  of  the  iron  core,  such  molecular 
motions  being  due  to  the  electric  currents  from  the  "  transmitter  "  (or 
telephone  spoken  to),  and  that  the  diaphragm  is  valuable  for  the 
purposes  of  strengthening  the  sound  (§  510)  and  transmitting  it  to 
the  ear  of  the  listener.  The  scientific  paper,  Nature,  says  that  care- 
ful investigation  leads  to  the  conclusion  that,  at  the  sending  station, 
the  evidence  of  molecular  action,  though  suggestive,  is  by  no  means 
conclusive,  whereas,  at  the  receiving  station,  the  existence  of  molec- 
ular as  well  as  mechanical  action  amounts  to  demonstration  and  is 
shown  to  be  considerable  in  amount. 

"  The  infinite  varieties  of  sound  arc  duo  to  the  subtile  capacity  for 
complex  motion  possessed  by  air  particles.  If  we  could  see  the  dance 
of  the  air  particles  when  music  is  executed,  it  would  be  a  picture  of 
mathematical  exactness  and  infinite  complication  that  has  no  analogy 
in  anything  we  observe.  It  has  always  been  regarded  as  one  of  the 
mysterious  miracles  of  vital  structure  that  the  drum  of  the  human 
ear  can  take  up  so  perfectly  this  rapid  stream  of  intricate  motions  in 
the  air,  thousands  of  tympanums  being  affected  alike,  while  the 
nerves  transmit  the  thrills  to  the  brain,  awakening  the  same  musical 
sensations  in  the  consciousness  of  as  many  persons  as  can  be  brought 
within  hearing.  The  chain  of  effects  is  wonderful  indeed,  but  the 
diaphragm  of  the  telephone  is  as  sensitive  as  the  living  tympanum 


APPENDIX. 


581 


to  all  the  delicate  refinements  of  sound.  Let  a  word  be  pronounced 
for  a  person  to  repeat;  the  telephone  will  hear  and  speak  it  a  hun- 
dred miles  away  in  a  tenth  part  of  the  time  that  the  listener  would 
need  to  utter  it." 

APPENDIX    P. 

The  Phonograph.— (See  §  508.)     The  appearance  of  this 
instrument  is  shown  in  the  accompanying  cut,  in  which  F  represents 


FIG.  409. 

the  mouthpiece  ;  C,  the  cylinder  covered  with  tin  -foil  ;  E,  the  axis 
with  a  thread  working  in  A,  one  of  the  two  supports.  The  mouth- 
piece, with  its  diaphragm  and  style,  may  be  moved  toward  the 
cylinder  or  from  it,  by  means  of  the  supporting  lever,  HG,  which 
turns  in  a  horizontal  plane  about  the  pin,  I. 


APPENDIX    Q. 

The  Sonometer.  —  (See  §  519.)  The  sonometer  box  may  be 
made  by  any  carpenter.  It  is  about  fifty-nine  inches  long,  4f  inches 
wide  and  4f  inches  deep.  The  ends  are  made  of  inch  oak  boards, 
the  sides  of  |  inch  oak  boards  and  the  top  of  |  inch  pine  board.  The 
top  should  be  glued  on  ;  no  bottom  is  needed  ;  the  box  may  sit 
directly  on  the  table.  Three  or  four  one-inch  holes  may  well  be 
bored  in  each  side-piece.  The  two  bridges,  shown  at  A  and  B  (Fig, 
268),  should  be  of  very  hard  wood  and  glued  to  the  cover  just  47  J 
inches  (120  centimeters)  apart,  measured  from  centre  to  centre.  The 
strings  may  be  such  as  are  used  on  bass-viols  ;  they  should  be  alike. 
Two  similar  pieces  of  piano-forte  wire  (large  size)  may  be  used.  The 
strings  may  be  stretched  by  weights  as  shown  in  the  figure  or  by 


582  APPENDIX. 

two  piano  string  pegs  turned  with  a  wrench  or  a  piano  tuner's  key. 
The  familiar  screw  arrangement  of  the  bass-viol  may  be  used  for  the 
purpose.  If  piano  wires  are  used  for  strings,  the  ends  must  be 
annealed  by  heating  them  red  hot  and  cooling  them  slowly,  so  that 
they  may  remain  fixed  when  wound  around  their  fastenings.  Lines 
should  be  drawn  across  the  top  of  the  box,  exactly  dividing  the  dis- 
tance between  the  middle  of  the  bridges  (at  which  points  the  strings 
are  supported)  into  halves,  thirds  and  quarters.  Provide  a  block 
of  wood,  about  two  inches  wide,  4|  inches  long  and  just  thick 
enough  to  slip  between  the  strings  and  the  top  of  the  box.  (See  Fig. 
279.) 

APPENDIX    R. 

Differential  Thermometer.— (See  §  547.)  Prepare  two 
boards,  each  5x7  inches  and  an  inch  thick.  Place  them  upon  end 
parallel  to  each  other,  7  inches  apart.  Connect  the  boards  by 
nailing  to  their  tops  two  thin  strips,  each  an  inch  wide  and  9  inches 
long.  The  strips  will  be  3  inches  apart.  This  is  our  stand.  For 
the  two  bulbs,  use  two  tin  oyster  cans  with  flat  sides.  To  the  centre 
of  one  end  of  each,  solder  a  tin  tube,  1|  inches  long  and  f  of  an 
inch  in  diameter.  Take  a  30-inch  piece  of  glass  tubing  that  will 
slide  easily  within  the  tin  tubes.  Bend  it  at  right  angles,  12  inches 
from  each  end,  like  the  tube  shown  iii  Fig.  289.  Color  a  little 
alcohol  with  red  aniline,  and  pour  into  the  bent  tube  enough  to  fill 
an  inch  or  two  above  each  bend.  Over  each  arm  of  the  bent  tube, 
pass  an  inch  of  snugly-fitting  rubber-tubing  and  slide  it  down 
about  8  inches.  Pass  the  arms  of  the  glass  tube  up  through  the 
tin  tubes  of  the  inverted  cans  as  far  as  they  will  go.  Slide  the 
rubber-tubing  upward  to  make  air-tight  joints  between  the  glass 
and  the  tin  tubes.  Place  the  cans  upon  the  horizontal  strips  of  the 
frame  already  made,  allowing  the  glass  tube  to  hang  between  the 
boards.  The  level  of  the  liquid  in  either  arm  may  be  marked  by  a 
thread  or  rubber  band  that  may  be  moved  up  or  down. 

APPENDIX   S. 

Cut-off  Engines. — With  a  plain  sliding  valve,  like  that 
described  in  §  637^  the  steam  pressure  is  evidently  the  same  at  the 
end  as  at  the  beginning  of  the  stroke  of  the  piston.  But  the  greatest 
economy  of  operation  is  attained  when  the  steam  is  so  used  that, 
when  the  piston  has  reached  the  end  of  its  stroke  and  the  exhaust 
valve  is  opened,  the  steam  pressure  is  but  little  if  any  above  that  of 


APPENDIX.  583 

the  atmosphere.  To  secure  this  economy,  the  Cut-off  Engine  has 
been  devised.  Here,  the  steam  is  not  admitted  to  the  cylinder  during 
the  full  travel  of  the  piston,  but  is  cut  off  at  an  earlier  or  later 
point  of  the  stroke,  the  steam  already  admitted  expanding  with 
decreasing  pressure  to  the  end  of  the  stroke.  The  engine  may  be 
built  so  as  to  cut  off  at  a  certain  fraction  of  the  stroke,  as  three- 
fourths,  obtaining  the  benefit  of  the  expansion  of  the  steam  for  the 
remaining  one-fourth.  'This  arrangement  is  called  a  fixed  cut-off. 

But  in  many  cases,  the  power  required  is  frequently  varying  with 
the  nature  of  the  work,  and  the  point  of  cut-off  best  adapted  to  one 
load  is  unfitted  to  another.  Hence,  the  desirability  of  being  able  to 
shift  the  point  of  cut-off  to  an  earlier  or  later  part  of  the  stroke. 
Many  devices  have  been  brought  forth  to  secure  this  object.  If  the 
shifting  be  done  by  hand,  the  arrangement  is  called  an  adjustable 
cut-off;  if  it  be  done  by  the  governor,  the  arrangement  is  called  an 
automatic  cut-off. 

APPENDIX    T. 

Telescopes.— (See  §§  731  and  732.)  In  estimating  the  efficiency 
of  a  telescope,  the  illuminating  power  must  be  considered  as  well 
as  the  magnifying  power.  The  brilliancy  of  the  image  depends 
largely  upon  the  diameter  of  the  object-glass  or  reflector.  It  is 
evident  that  of  two  telescopes  having  equal  magnifying  power,  the 
one  that  has  the  larger  "  aperture  "  will  receive  and  transmit  more 
luminous  rays  and,  hence,  cause  the  image  to  be  better  illuminated 
and  more  distinct. 


NUMBERS   REFER  TO   PARAGRAPHS,    UNLESS  OTHERWISE 
INDICATED. 


Aberration,  Chromatic,  711. 

Spherical,  698.  [398. 

Abreast  method  of  joining  voltaic  cells, 

Absolute  electric  units,  -320. 

magnetic    "    450, 451. 
pitch  of  sound,  523. 
"        units,  68,  154,  450,  451. 
zero  of  temperature,  558. 

Absorption  and  radiation  of  heat  and 
light,  721,  722 ;  Absorption  of  heat,6i8. 

Accordeon,  535  (a). 

Achromatic  lens,  712, 

Acoustic  tubes,  495. 

Actinic  rays,  719. 

Adhesion  defined,  46. 

Aerial  ocean,  271. 

Aeriform  body  denned,  57,  61. 

Aether,  608. 

Affinity,  Chemical,  633. 

Air-chamber,  297. 

Air-pump,  288-293. 

Air,  Weight  of,  272. 

Alphabet,  Morse's,  445. 

Amalgam,  302  (a). 

Amalgamating  battery  zincs,  388. 

American  wire  gauge,  App.  I. 

Ampere,  385. 

Ampere-volt,  475. 

Amplitude  of  vibration,  140,  481,  493. 

Analysis  of  light,  700-703. 

"  sounds.  Exp.  16,  p.  404 ;  529. 

Analyzer  of  polariscope,  737  («). 
Aneroid  barometer,  280. 
Angle  of  incidence,  97. 
Anion,  411.     . 
Annunciators,  444. 


Anode,  411. 

Apparent  direction  of  bodies,  659. 

Archimedes'  principle,  238-239. 

Arc  lamps,  467. 

Armatures  for  magnets,  424,  449,  464. 

Arrangement  of  voltaic  cells,  Best,  40* 

Artificial  magnet,  310,  424. 

Ascending  bodies,  132. 

Astatic  galvanometer,  418. 

"       needle,  439  (a). 
Astronomical  telescope,  731, 732. 
Athermanous,  617. 
Atlantic  cable,  359,  360. 
Atmospheric  electricity,  365-370. 

pressure,  273,  275,  277. 
Atom  denned,  6. 
Attraction,  Capillary,  235. 

Electric,  303,  321  («). 

Forms  of,  7. 

"  Magnetic,  427-449. 

Attwood,  122. 
Aurora  borealis,  370. 
Australis,  The  Aurora,  370. 


Balance,  175. 

"        False,  176. 
Balloons,  App.  G. 
Barker's  mill,  264,  App.  F. 
Bar  magnet,  424. 
Barometer,  274,  278-280. 
Baroscope,  281. 
Battery,  Best  arrangemement  of,  400. 

"       Brush,  415  (</). 

"        Faure,  415  (a). 

"       Galvanic.     (See  Voltaic.) 

"       Intensity,  400  (£). 


INDEX. 


585 


Numbers  refer  to  paragraphs,  unless  other-wise  indicated. 


Battery,  Leyden,  358. 

"       of  high  resistance,  399. 

u       of  low  resistance,  400. 
Quantity,  400  (6). 

"       Requisites  of  a  good,  401. 

"       Secondary,  415. 

"       Voltaic,  398-402. 

44       zincs,  Amalgamating,  388. 
Beam  of  light,  648. 
Beats,  516,  517 
Beaume's  hydrometer,  252. 
Bell,  Electric,  447. 
Bellows,  Hydrostatic,  222. 
Bent  levers,  173. 

Best  arrangement  of  voltaic  cells,  402. 
Bi-chromate  of  potassium  cell  or  bat- 
tery, 392. 

Biot's  hemispheres,  Exp.  28,  p.  212. 
Birmingham  wire  gauge  (B.  W.G.)  Ap.  I. 
Blake  transmitter,  507. 
Blind  spot  of  eye,  724. 
Boiling-point,  544,  566-575. 
Borealis,  The  Aurora,  370. 
Bramah's  press,  223. 
Breast  wheel,  262. 
Brittleness  defined,  49. 
Broken  magnets,  430. 
Brown  &  Sharpe  wire  gauge,  App.  I. 
Brush,  battery,  415  (d). 
';     dynamo,  465. 
"     laoips,  467. 
Bunsen's  air-pump,  291. 

"  cell  or  battery.  397. 
Burglar  alarms,  Electric,  444. 
B.  W.  G.,  App.  I. 


Callaud  cell  or  battery,  395. 
Calorie,  471,  579. 
Calorescence,  718  (a). 
Calorific  powers,  634. 
Calorimeter,  596  (a). 
Camera  obscura,  650. 

"       The  photographer's,  723. 
Candle,  Standard,  Ex.  5,  p.  482. 
Capacity,  Dielectric,  352  (S). 

"         Electric,  330. 

"    How  measured,  App. 

M(5). 
Capillary  attraction,  235. 

"         phenomena,  236. 
Cathetal  prism,  686  (c). 
Cathion,  411. 
Cathode,  411. 


Cells,  Voltaic,  Best  arrangement  of,  402, 

"        Varieties,  39°-397- 
Centrifugal  force,  74,  77. 
C.  G.  S.  units,  69, 154,  450,  451. 
Changes,  Chemical,  u. 

"       of  condition  of  matter,  59. 

l>        Physical,  10. 
Characteristic  properties,  19,  21. 
Characteristics  of  magnets,  428. 
Charge,  Residual,  356 ;  App.  J. 
Charging  with  electricity  by  conduc- 
tion, 331. 
Charging  with   electricity  by  contact, 

33i- 
Charging  with  electricity  by  induction, 

332-335- 

Chemical  affinity,  633. 
"  changes,  u. 
"  effects  of  electric  current, 

410. 

"         properties,  15. 
44         unit  of  matter,  6. 
Chromatic  aberration,  711. 
Chromatics,  699. 
Circuit,  Electric,  305. 
Clarionet,  535  (a),  536. 
Clouds,  Electrified,  365-368. 
Coercive  force,  425. 
Cohesion  defined,  46. 
Coils,  Induction,  457-460. 
44     Primary,  457. 
"     Resistance,  App.  M  (i). 
"     Ruhmkorff,  459. 
"     Secondary,  457. 
Coincident  waves,  511. 
Color  blindness,  725. 
44     of  bodies,  705. 
Colors,  by  polarized  light,  745  (a). 
44       Complementary,  705  (6). 
"       of  the  sky,  705  (<:). 
"       Prismatic,  700. 
Combs,  344. 
Commercial  efficiency  of  dynamo.  Ex. 

4,  p.  366. 

Communicating  vessels,  234. 
Commutator,  459  (</),  465. 
Compass,  309,  439  (a). 
Compensating  pendulum,  149. 
Complementary  colors,  705  (£). 
Composition  of  forces,  80,  88. 

14  "   white  light,  704. 

Compound  machines,  211. 

44          tones,  529. 
Compressibility  defined,  43. 


586 


INDEX. 


Numbers  refer  to  paragraphs^  unless  otherwise  indicated. 


Concave  lens,  687,  691,  697. 
Condensation  of  electricity,  350. 
Condensers,  292,  351,  360;  App.  M  (5). 
Conditions  of  matter,  53. 

"  "      "        Changes  of,  59. 

Conduction  of  electricity,  324. 

"  heat,  603. 

Conductive  discharge,  364. 
Conductors  of  electricity,  324,  476. 
Conjugate  foci,  503,  667,  690,  691. 
Conservation  of  energy,  749.  [693. 

Construction  for  images,  662,  670,  673, 
Continuous  sounds,  490. 
Convection  of  heat,  606. 
Convective  discharge,  363. 
Convertibility  of  energy,  159,  470-475, 

581,582,  746. 

Convex  lens,  687-690,  692-696. 
Copper  plating,  Exp.  78,  p.  285. 

"      voltameter,  Exp.  78,  p.  285. 

"      wire,  App.  I. 
Correlation  of  energy,  627,  750. 
Coulomb,  387. 
Coulomb's  law,  319  (2). 
Critical  angle,  682. 
Crooke's  tubes,  Exp.  71,  p.  250. 
Current,  Electric,  314,  374,  377,  405  -418, 

456-465,  468,  469-476- 
Current,  Electric,  Effects  of,  405-418. 

"  "         Unit  of,  385. 

"        electricity,  306,  374,  377. 

"        Extra,  458. 
Curves,  Magnetic,  433. 
Cut-off  engines  (steam),  App.  S. 
Cycloidal  pendulum,  144. 


Daniell's  cell  or  battery,  394. 
Dark  Foci,  720. 
Declination,  Magnetic,  441. 
Deflection  of  magnetic  needle,  417. 
Delany's  telegraph,  446. 
Density,  Electric,  342. 
Diamagnetic  substances,  431. 
Diathermancy,  617. 

Dichromate  of  potassium  cell  or  bat- 
tery, 392. 
Dielectric  capacity,  352. 

"        machine,  346,  347. 
Dielectrics,  352,  App.  J. 
Differences  of  potential,  328,  329. 
Differential  galvanometer,  App.  L  (4). 

••          thermometer,  547,  App.  R, 


Diffraction,  714. 
Diffused  light,  657. 
Diffusion  of  heat,  602. 
Dip,  Magnetic,  440. 
Dipping  needle,  439,  440. 
Direction,  Line  of,  65,  114. 

"         of  bodies,  Apparent,  659. 
Discharge,  Modes  of  electric,  361-364. 
Discharger   for    electricity,    355,    358 

Exp.  56,  p.  244. 
Dispersion  of  light,  701. 
Disruptive  discharge,  362. 
Dissipation  of  energy,  747. 
Distance,  How  estimated,  726. 
Distillation,  576-578. 
Distribution  of  electricity,  342. 
"  magnetism,  426. 
Divided  electric  circuits,  404. 
Divisibility  defined,  41. 
Divisions  of  matter,  3. 
Double  refraction,  743. 
"      weighing,  177. 
Downward  pressure,  225,  226. 
Ductility  defined,  51. 
Duplex  telegraph,  446. 
Duration  of  electric  spark,  368. 
Duty  of  dynamo,  Ex.  3,  p.  366. 
Dynamics  defined,  63. 
Dynamo  electric  machine,  465. 
Dynamos,  465. 

"  Commercial    efficiency    of, 

Ex.  4,  P.  366. 
Duty  of,  Ex.  3,  p.  366. 
Dyne  defined,  69. 


Ear,  Range  of,  517. 
Earth  a  magnet,  437. 
Ebullition,  566-575. 
Eccentric,  638. 
Echo,  504. 

Edison's  electric  lamp,  466  (a). 
"       meter ,-41 1  (£). 
Effects  of  electricity,  405-418,  470-476. 
Efficiency    of   dynamo,    Commercial, 

Ex.  4,  p.  366. 

Efficiency  of  steam  engine,  641  (a). 
Egg-shell  conductor,  332  (6). 
Elasticity,  45. 
Electric  action,  Law  of,  319. 

"       attraction,  303,  321  (a), 

"       battery,  358. 

"       bell,  447. 


INDEX. 


587 


Numbers  refer  to  paragraphs,  unless  otherwise  indicated. 


Electric  bomb,  Exp.  53,  p.  243. 

"       brush,  362  ;  Exp.  35,  p.  23^. 
"       capacity,  330. 

Unit  of,  359. 
"       charge,  314,  341. 
"       chime,  Exp.  41,  p.  240. 
"       circuit,  305,  377. 
"  .     condensers,  351. 
"       conductors,  324,  476. 
"       current,  314,  374,  377,  405-418, 

456-465,  468,  469-476. 
"       density,  342. 
"       discharge,  361-364. 

effects,  405-418,  470-476. 
glow,  362  ;  Exp.  35,  p.  233. 
"       induction,- 332-335. 
"       kite,  Exp.  45,  p.  241. 
lamps,  466,  467. 
light,  465-467. 

44       machines,  343-349,  465. 
u       manifestations,  314. 
'4       measurements,  App.  M. 
44       motors,  465  (<:),  473. 
44       orrery,  Exp.  49,  p.  242. 
pendulum,  304,  323  (a). 
44       portrait,  Exp.  57,  p.  244. 
44       potential,  326-330,  384. 
"       quantity,  387. 
44       repulsion,  304,  321  (a). 
44       resistance,  379,  App.  K,  App. 

M  (1-3). 

44       resistance,  Unit  of,  380. 
"       separation,  316,  332. 
4'      series,  318. 
14       shock,  409. 

44       spark,  362;  Exp.  35,  p.  233 ;  460. 
44        swing,  Exp.  43,  p.  241. 

telegraph,  444-446. 
44       tension,  326. 
44       testing,  App.  M  (i). 
41       transmission  of  power,  474. 
44       trembler,  447. 
44       units,  320,  321,  329,  330,  359. 
44       whirl,  Exp.  48,  p.  241. 
Electricity  and  energy,  340,   372,  376, 

470-475. 

44          and  heat,  470-472,  476. 
44         Atmospheric,  365-370. 
44          Condensation  of,  350. 
*4         Condensers  of,  351. 
44          Conductors  of,  324. 
44         Current,  306,  314,  374,  377. 
44  44         Unit  of,  385. 


Electricity,  Distribution  of,  341,  342. 
44          Effects  of,  405-418,  470-476. 
Frictional,  302-304,  314-370. 

Laws  of,  319. 
44          Galvanic,  see  voltaic. 

Induced,  311,  374,  456-469. 
Nature  of,  313. 
Static,  see  frictional. 
44          Tests  for,  322. 
Theory  of,  337. 
Thermo-,  311,  374,  419-422. 
Two  kinds  of,  315,  317. 
"          Voltaic,  305,  306,  373-418 
Electrics,  325. 
Electrodes,  378,  411. 
Electrolysis,  410-415. 
Electrolyte,  410. 
Electrophorus,  338-340. 
Electro-chemical  series,  413. 
44       gilding,  412. 
44       magnet,  307,  442-449- 
44       magnetic  engines,  473. 

'4        units,  320,  451. 
44       metallurgy,  412. 
44       motive  force,  see  E.  M.  F. 
negative,  413. 
plating,  412. 
44       positive,  413, 
Electro -static  distribution,  342. 

44    induction,  332-335, App.  J 
4i    units,  320,  321,  329.  330. 
Electrotyping,  412. 

Electroscope,  323,  338  (b)  •  Ex.  n.  p.  223. 
E.  M.  F.  (electromotive  force),  327, 382. 
E.  M.  F.,  How  measured,  App.  M  (4). 
E.  M.  F.  of  battery,  399  (a),  400  («). 
E.  M.  F.  of  polarization,  414. 
E.  M.  F.,  Relation  to  conductors,  476. 
E.  M.  F.,  Unit  of,  382. 
Endless  screw,  210. 
Energy  a  constant  quantity,  160. 

and    electricity,  340.  372,  376, 

470-475- 

14  and  magnetism,  455. 
14  Conservation  or,  749. 
44  Convertibility  of,  159,  470-475 

581,  582,  746. 

"        Correlation  of,  627,  750. 
14       defined,  151. 
44        Dissipation  of,  747. 
44        Formulas  for  kinetic,  157. 
"        Indestructibility  of,  163. 
Solar,  746. 


588 


INDEX. 


Numbers  refer  to  paragraphs,  unless  other-wise  indicated. 


Energy,  Types  of,  158. 

Varieties  of,  748. 
Engine,  The  steam,  635-643. 
English  measures,  23. 
Equator,  Magnetic,  426. 
Equilibrant,'  86. 

Equilibrium,  110-113;  of  liquids,  233. 
Equipotential  surface,  329  (a). 
Erg  defined,  154. 
Ether,  608. 

Evaporation,  564,  565. 
Expansibility  defined,  44. 
Expansion  by  heat,  548-557. 
Extension  defined,  22. 
Extra  current,  458. 
Eye,  The  human,  724-727. 


Fahrenheit's  hydrometer,  251. 

"  thermometer,  545. 

Falling  bodies,  119. 

"        Laws  of,  129. 
Fall  of  electric  potential,  384. 
False  balance,  176. 
Farad,  359. 
Faraday's  bag,  Exp.  30,  p.  213. 

"  cage,  341  (£). 

Farsightedness,  727. 
Faure  battery,  415  (at). 
Field,  Magnetic,  433. 

"     of  force,  App.  N. 
Fife,  536. 

Fire  alarms,  Electric,  444. 
Floating  bodies,  240. 
Flow  of  liquids,  254-259. 
Fluid  defined,  60,  61. 

"     displaced  by  immersed  solid,  237. 
Fluorescence,  719. 
Flute,  536. 
Fly-wheel,  639. 
Focus,  Dark,  720. 

"      of  heat,  620,  6?  i. 

"      "  light,  664,  666-668,  689-691 

"      "  sound,  501. 
Foot-pound  defined,  153. 
Foot-pound-second  unit,  68. 
Force,  Absolute  unit  of,  68. 

"      Centrifugal,  74,  77. 

"      C.  G.  S.,  unit  of,  69. 

"       Constant,  118. 

"      defined,  64. 

•'      Elements  of  a,  65. 

"      Field  of,  App.  N, 


Force,  F.  P.  S.  unit  of,  68. 
"       Gravity  unit  of,  67. 
"      Kinetic  unit  of,  68. 
"       Measurement  of,  66. 
"      of  gravity  resolved,  199. 
"      pump,  297. 
'•      Tube  of,  App.  N. 
Forces,  Composition  of,  80.  . 

"       Graphic  representation  of,  81. 
"      Moments  of,  171. 
*'       Parallogram  of,  82. 
"       Parallelepiped  of,  90. 
"       Polygon  of,  89. 
tl      Resolution  of,  91. 
"       Triangle  of,  87. 
Forms  of  attraction,  7. 

"      "  motion,  8. 

Formulas,  Mathematical,  App.  A. 
F.  P.  S.  unit  of  force,  68. 
Fraunhofer's  lines,  703. 
Freezing  mixtures,  586. 

"        point,  543. 
Friction,  212-214. 

"        develops  heat,  629. 
Frictional  electricity,  302-304,  314-370. 
Fuel,  641  (a). 

Fundamental  tones,  524,  525. 
Fusion  of  ice,  Heat  equivalent  of,  593. 
Fusing  point,  562. 

G 

Galileo,  121,  730. 
Galvanic,  see  voltaic. 
Galvani's  experiment,  408. 
Galvanometer,  Astatic,  418. 

"  Differential,  App.  L  (4). 

"  Mirror,  App.  L  (3). 

"  Potential,  App.  M  (4*:). 

"  Sine,  App.  L  (i). 

M  Tangent,  App.  L  (2). 

Gamut,  521. 
Gas  defined,  58. 
Gases,  Kinetic  theory  of,  62, 
"      Specific  gravity  of,  248. 
"      Tension  of,  62,  269,  282-287,  559- 
"      Type  of,  270. 
Gauges,  Wire,  App.  I. 
Geissler's  tubes,  Exp.  70,  p.  249. 
Gold  leaf  electroscope,  323. 
Gore's  railway,  Exp.  74,  p.  279. 
Governor  for  steam  engines,  639. 
Graduation  of  thermometers,  542. 
Gram  defined,  36. 
Graphic  representation  of  forces,  81. 


INDEX. 


589 


Numbers  refer  to  paragraphs,  unless  otherwise  indicated. 


Gravitation  defined,  98  ;  Laws  of,  100. 
Gravity  cell  or  battery,  395. 

'*       Centre  of,  107-110. 

"       defined,  102. 

*'      Force  of,  resolved,  109. 

"       Increment  of,  127. 

"      Specific,  241-253. 

"       unit  of  force,  67. 
Grenet  cell,  392. 
Grove's  cell  or  battery,  396. 
Guitar,  518. 

H 

Haloes,  714. 

Hardness,  47. 

Harmonics,  524. 

Harp,  518. 

Head  of  liquids,  254. 

Heat,  Absorption  of,  721,  722. 

"     Conduction  of,  603. 

u     Convection  of,  606. 

"     defined,  538. 

"     Diffusion  of,  602. 

*'     Effect   on    electrical    resistance, 
App.  K  (3). 

"     equivalent  of  chemical  union,  634. 

"       "    of  fusion  of  ice,  593. 

"        "    of  vaporization  of  water,  594. 

"      from  friction,  629. 

"         "    percussion,  628. 

«'      Latent,  583-595- 

"      Luminous,  617. 

"      Mechanical  equivalent  of,  631. 

"     Obscure,  617. 

"      Radiation  of,  607,  610,  721,  722. 

'*     Reflection  of,  619. 

"     Refraction  of,  621. 

"     Sensible,  581,  582. 

**     Specific,  596-601. 

"     unit,  579. 
Heating  powers,  634. 
Heliostat,  655. 
Helix,  416  (b\  442. 
Helmholtz's  resonators,  514,  529  (a). 
Hollow  conductors,  341. 
Holtz  electric  machine,  348,  349. 
Homogeneous  light,  713. 
Horizontal  needle,  439. 
Horse-power,  155,  475. 
Horse-shoe  magnet,  424,  443. 
Human  eye,  724-727. 
Hydraulic  motors,  384  (a). 
Hydrokinetics,  254. 
Hydrometer,  249-252. 


Hydrostatic  bellows,  222. 
"  paradox,  229. 

"          press,  223. 


Ice,  Heat  equivalent  of  fusion  of,  593. 

Iceland  spar,  743. 

Images,  Construction  for,  662,  670,  673, 

693- 

*'       Inverted,  650, 672,  674,  694,  695. 

"      Multiple,  663. 

4i      Projection  of,  671,  694,  695,  734. 

"      Real,  669-672,  694,  695,  734. 

"       Virtual,  660,  673,  675,  696,  697. 
Impenetrability  defined,  31. 
Incandescence  lamp,  466. 
Incidence,  Angle  of,  97. 
Inclination,  Magnetic,  440. 
Inclined  plane,  198-204. 
Incompressibility  of  liquids,  215. 
Increment  of  velocity,  127. 
Indestructibility  of  energy,  162. 
"  "    matter,  37. 

Index  of  refraction,  678. 
Induced  electricity,  311,  374,  456-469. 
Induction  coils,  457-460. 
Induction,  Electro-dynamic,  456-469. 

"    static,  332-335,  App.  J. 
"         Magnetic,  435,  436. 
Inertia  defined,  38. 
Insulators,  324. 

Intensity  of  electric  current,  385,  387  (a). 
"  light,  654. 

"        "  sound,  493,  494. 
Interference  of  light  713. 

"  sound,  515. 
Intermittent  springs,  301. 
Internal  reflection  of  light,  681. 

"       resistance,  383,  399,  400. 
Inverted  images,  650,  672,  674,  694,  695. 
Invisibility  of  light,  658. 
Ions,  411. 
Irradiation,  715. 

J 

Jar,  Leyden,  353-357- 
Joining  voltaic  cells,  398-402. 
Joint  resistance,  Electric,  404  (£). 
Joule,  The,  471. 
Joule's  equivalent,  631,  632. 
"      law,  471. 

K 

Kathion,  411. 
Kathode,  411. 


590 


INDEX. 


Numbers  refer  to  paragraphs,  unless  otherwise  indicated. 


Kinetic  energy,  Formula  for,  157. 
"       theory  of  gases,  62. 
"       unit  of  forces,  68,  69. 


Lamps,  Electric,  466,  467. 
Latent  heat,  583-595. 
Lateral  pressure,  230,  231. 
Leclanche  cell  or  battery,  393. 
Lenses,  687,  712. 
Leslie's  cube,  619,  623. 
Lesser  calorie,  471,  579. 
Lever,  Classes  of,  169. 

"      Compound,  178. 

u      denned,  168. 

"      Laws  of,  170. 
Leyden  battery,  358. 

"      Jar,  353-357;  Ex-  "»  P-  252;  Ap.  J. 

"        "  and  bells,  Exp.  42,  p.  241. 
Lifting-pump,  294. 
Light,  Absorption  of,  721,  722. 

"     Analysis  of,  700-703. 

'*      Composition  of  white,  704. 

"     defined,  644. 

"     Diffused,  657. 

"     Dispersion  of,  701. 

"     Effect  on  electrical  resistance, 
App.  K  (4). 

"      Electric,  720. 

"•     Homogeneous,  713. 

'•     Invisibility  of,  658. 

"      Polarization  of,  737-747. 

u      Radiation  of,  721,  722. 

"     Rectilinear  motion  of,  649. 

"     Reflection  of,  655-675. 

"     Refraction  of,  676-719. 

"     Synthesis  of,  704. 

"      Velocity  of,  653. 
Lightning,  368  ;  rods,  369. 
Line  of  no  variation,  441. 
Lines  of  force,  App.  N. 
Lines  of  magnetic  force,  433. 
Liquid  denned,  55,  61. 

"       rest,  Condition  of,  232. 
Liquids,  Equilibrium  of,  233.  [259. 

"       flowing    through   pipes,    257, 
"       in  communicating  vessels,  234. 
'•        Incompressibilityof,  215. 
"        Spouting,  254-256. 
Liter  defined,  29. 
Loadstone,  see  lodestone. 
Local  action  in  batteries,  388. 
Lodestone,  310,  423. 


Long  coil  electric  instruments,  403. 
Loudness  of  sound,  493. 
Luminiferous  ether,  608. 
Luminous  bodies,  645. 

"          effects    of  electric    current, 
407. 

"         globe,  Exp.  68,  p.  248. 

"         jar,  Exp.  66,  p.  247. 

"         pane,  Exp.  67,  p.  248. 

"         spectrum,  717. 

"         tube,  Exp.  68,  p.  248. 

M 

Machine  cannot  create  energy,  164, 165. 
"       defined,  163. 
"        Laws  of,  167. 
Uses  of,  166. 
Machines,  Compound,  211. 

Electric,  343-349.  465- 
Magic  lantern,  734. 
Magnet,  Artificial,  310,  424. 
"        Broken,  430. 

Electro-,  307,  442-449- 
"        How  made,  448. 
"        Laws  of,  429. 
•   "        Molecular  changes  in,  453. 
"        Natural,  310,  423. 
"       Permanent,  308. 
"       Temporary,  307. 
Magnetic  attraction,  427-449. 
"          charts,  441  (a). 
"         compass,  309,  439  («). 

curves,  433. 
"         declination,  441. 
"         effects    of    electric   current, 

416. 
"         equator,  426. 

field,  433. 

"        force,  lines  of,  433. 
"         inclination  or  dip,  440. 
"         induction,  435,  436. 
*'         meridian,  441,  App.  L  (2). 
"         needles,  417,  439. 
"         neutral  point,  426. 
poles,  426,  438. 
retentivity,  425. 
screens,  432. 
substances,  431. 
units,  450. 
variation,  441. 
Magnetism,  307,  423-455- 

"          and  energy,  455. 
"          Distribution  of,  4a6, 


INDEX. 


591 


Numbers  refer  to  paragraphs,  unless  otherwise  indicated. 


Magnetism,  Residual,  443  (a). 

Terrestrial,  437,  438. 
"  Theory  of,  454. 

Magnetite,  423. 
Magnetization,  434,  448. 
Magnetized  substances,  431. 
Magneto-electric  current,  462,  463. 
Magnetos,  465  (£). 
Magnifying-glass,  728. 
Malleability  defined,  50. 
Malus's  polariscope,  742. 
Manipulator,  415  (d). 
Marcet's  globe,  572. 
Mariner's  compass,  309,  439  (a). 
Mariotte,  284,  285. 
Mass  defined,  4,  6. 
Mathematical  formulas,  App.  A. 
Matter,  Conditions  of,  53. 

"       defined,  2. 

44      Divisions  of,  3. 

"       Properties  of,  13. 

44       Radiant,  59  (b) ;  Exp.  71,  p.  250. 
Measurement   of    electric    resistance, 

App.  M.  (2  and  3). 

Measurement  of  E.  M.  F.,  App.  M  (4). 
Measures,  23-30,  34-36. 
Mechanical  effects  of  electric  current, 

405,  473-475- 

Mechanical  equivalent  of  heat,  631. 
Megohm,  380. 
Melting  points,  562. 
Meter  defined,  25. 
Metric  measures,  24-30,  35,  36. 
Microhm,  380. 
Microscope,  728,  729. 
Microvolt,  382. 
Mil,  381  (*). 

Millecalorie,  see  lesser  calorie. 
Milliampere,  385. 
Mirror  galvanometer,  App.  L  (3). 
Mirrors,  Concave,  664-674. 

"       Convex,  675. 

"       Parabolic,  666  (a). 

"       Plane,  660-663. 
Mobility  defined,  40. 
Molecular  changes  in  magnets,  453. 

'•         velocity,  62  (a). 
Molecules  defined,  5,  6. 
Momentary  sounds,  490. 
Moment  offerees,  171,  172. 
Momentum  defined,  70. 
Morse's  alphabet,  445. 

44       telegraph,  444. 


Motion,  Forms  of,  8. 

"       Newton's  laws  of,  72,  73,  78, 93. 

"•       of  the  pendulum,  139. 

"       Reflected,  96,  97. 

"       Resultant,  79. 
Motors,  Electric,  465  (c),  473. 

"       Hydraulic,  384  <»• 
Multiple  arc  method  of  joining  voltaic 

cells,  398. 

Multiple  images,  663. 
Multiplex  telegraph,  446. 
Music,  491. 
Musical  instruments,  530-536. 

"      scale,  520,  521 ;  strings,  518,  519. 

X 
Natural  magnet,  310,  423. 

44      philosophy  defined,  12,  162. 

11      sines,  Table  of,  App.  L  (2). 

"       tangents,  Table  of,  App.  L  (i). 
Nature  of  electricity,  313. 
Nearsightedness,  727. 
Needles.  Magnetic,  417,  439. 
Negative  (  —  )  electricity,  317. 
Neutral  point,  Magnetic,  426. 
Newton's  disc,  Exp.  2,  p.  519. 

"         laws  of  motion,  72,  73,  78,  93. 

"         rings,  713. 
Nicholson's  hydrometer,  250. 
Nicol's  prism,  744. 
Nodal  points  or  nodes,  524-527,  536. 
Noise  and  music,  491. 
Non-luminous  bodies,  645. 

O 

Obscure  heat,  617. 

"       rays,  617,  718,  720. 
Ocean,  The  aerial,  271. 
Oersted's  apparatus,  417. 
Ohm,  380. 
Ohm's  law,  386. 
Opaque  bodies,  646. 
Opera-glass,  730. 
Optical  angle,  726. 

"      centre,  688. 
Organ  pipes,  516  («),  534. 
Oscillation,  Centre  of,  141. 

41          of  pendulum,  140. 
Overshot  wheel,  261. 
Overtones,  524,  526,  527. 


Papin's  digester,  571. 
Paradox,  Hydrostatic,  229. 
Parallel  joining  of  cells,  398. 


592 


INDEX. 


Numbers  refer  to  paragraphs,  unless  otherwise  indicated. 


Parallelogram  offerees,  82. 
Parallelepiped  of  forces,  90. 
Pascal,  217,  218,  221,  276. 
Peltier  effect,  422. 
Pencil  of  light,  648. 
Pendulum,  Compensation,  149. 

"         Compound,  138. 

"         Cycloidal,  144. 

"         Electric,  304,  323  (a). 

"         Laws  of,  143,  145,  146. 

"         Motion  of  the,  139. 

"         Real  length  of,  142. 
Simple,  137. 

"         The  second's,  147. 

"         Uses  of,  148. 
Percussion  develops  heat,  628. 
Permanent  magnet,  308. 
Persistence  of  vision,  725. 
Philosophy,  Natural,  defined,  12,  162. 
Phonograph.  508,  App.  P. 
Photographer's  camera,  723. 
Photophone,  App.  K  (4). 
Physical  change,  10. 

"        properties,  14,  15. 
"        science,  9. 
"        unit  of  matter,  5. 
Physics  defined,  12,  162. 
Physiological    effects   of  electric  cur- 
rent, 409. 

Piano,  518,  523  (b)  ;  Exp.  16,  p.  404. 
Pipes,  Musical,  531-536. 
Pitch  of  sound,  496-499. 

"      "      "        Absolute,  523. 
Plane,  Inclined,  198-204. 
Plate  electric  machine,  344,  345. 
Plating,  Electro  ,  412. 
Pneumatics  defined,  268. 
Pointed  conductors  of  electricity,  342. 
Polar iscope,  742,  745. 
Polarization  colors,  745  (a). 

"          Electric,  332,  336. 
E.  M.  F.  of,  4x4. 

"          of  batteries,  389. 

«*  of  light,  737-747- 

Polarizer,  737  (a). 
Poles,  Electric,  738. 

•*      Magnetic,  426,  438. 
Polygon  of  forces,  89. 
Porosity  defined,  42. 
Porte-lumiere,  655,  note. 
Positive  ( + )  electricity,  317. 
Potassium  di-chromate  cell  or  battery, 
392. 


Potential,  Electric,  326,  327-330,  384. 

"        galvanometer,  App.  M  (4*:) 
Power  defined,  155. 

"       Electric  transmission  of,  474. 
Press,  Hydrostatic,  223. 
Pressure,  Atmospheric,  273,  275,  277. 
u         Downward,  225,  226. 
"         Gaseous,  62,  269,  282-287. 
"         Lateral,  230-231. 
"         of  vapors,  568. 
"         Transmission  of,  by  liquids, 

216. 

"         Upward,  227,  228. 
Primary  coils,  457. 
Prince  Rupert  drops,  App.  D. 
Principal  axis,  664,  688. 

"         focus,  664,  666,  689. 
Prismatic  colors,  700. 
Prisms,  686,  718,  719, 744. 
Projectiles,  133. 

"         Path  of,  135. 
"         Time  of,  136. 
Proof-plane,  333  (a)  ;  Exp.  29,  p.  212. 
Propagation  of  sound,  484. 
Properties,  Characteristic,  19,  21. 
"         Chemical,  15. 
'*•        of  matter,  13. 
"         Physical,  14,  15- 
**         Universal,  18,  20. 
Provisional  theory  of  electricity,  337. 
Pulley,  192,  197. 
Pump,  Air,  288,  293. 
"      Force,  296,  297. 
"      Lifting,  294. 
Pure  spectrum,  702. 
Q, 

Quadruplex  telegraph,  446. 
Quality  of  sound,  528. 
Quantity  of  electricity,  387. 
Quartz  prism,  719. 

R. 

Radiant  energy,  484,  500,  607,  644. 
"       heat,  610. 

"      matter,  59  (£) ;  Exp.  71,  p.  250. 
Radiation  and  absorption  of  heat  and 

light,  721,  722. 

Radiation  of  sound,  484,  485,  500, 
Rainbow,  706-710. 
Random,  134. 
Range,  134. 
Rays,  Actinic,  719. 

"      Heat,  610,  616,  718. 
"     Luminous,  717. 


INDEX. 


593 


Numbers  r^fer  to  paragraphs,  unless  otherwise  indicated. 


Rays,  Obscure,  617,  718,  719. 
"     of  light,  647. 
"     of  sound,  500. 
"     Thermal,  718. 
"      Ultra-red,  718. 
"     Ultra-violet,  719. 
Reaction,  72,  93,  94,  95. 
Reed  pipes,  535. 
Reflected  motion,  96,  97. 
Reflecting  telescope,  732. 
Reflection  of  heat,   619,  620. 
"  light,  655-675. 
"         "  sound,  502-504. 
"        Total  internal,  681,  682. 
Refracting  telescope,  731. 
Refraction,  Double,  743. 
"         Index  of,  678. 
"         of  heat,  621. 
"          "  light,  676-719. 
"          "  sound,  500. 
Refractors,  Kinds  of,  684. 
Reinforcement  of  sound    511-514,  516, 

517- 

Relay,  Telegraphic,  445  (V). 
Repeater,  Telegraphic,  445  (</). 
Repulsion,  Electric,  304,  321  (a). 
Requisites  of  a  good  battery,  401. 
Residual  electric  charge,  356,  App.  J. 

"        magnetism,  443  (a). 
Resistance  box  and  coils,  App.  M  (i). 

"          Electric,  379,  App.  K. 

"  "        Measurement    of, 

App.  M. 

"  "        Unit  of,  380. 

"          Internal,  383,  399,  400. 

*4          Specific,  App.  K  (2). 
Resolution  offerees,  91,  199. 
Resonance,  513. 
Resonators,  514,  529  (a). 
Resultant  motion,  79,  85. 
Retentivity,  425. 
Rheostat,  App.  M  (zb). 
Rivers,  Flow  of,  258. 
Rock  salt  prism,  718. 
RuhmkorfTs  coil,  459. 
Rupert  (Prince)  drops,  App.  D. 

• 

Safety-valve,  640. 
Savart's  bell  and  resonator,  513  (a). 
Scale,  Musical,  520-523. 
Science  defined,  i. 

"      Physical,  9. 
Screens,  Magnetic,  432. 


Screw  defined,  208. 

"     Endless,  210. 

*'     Law  of,  209. 
Secondary  axis,  664,  688. 
"         battery,  415. 
"         coils,  457. 
"         foci,  689  (£). 
Selective  absorption,  618. 
Selenium,  App.  K  (4). 
Sensible  heat,  581. 
Series  joining  of  cells,  398. 
Shadows,  651. 

Short  coil  electric  instruments,  403. 
Shunts,  404, 
Silver  plating,  412. 
Simple  and  compound  tones,  529. 
Sine  galvanometer,  App.  L  (2). 
Sines,  Natural,  Table  of,  App.  L  (2). 
Siphon,  298-300. 
Size,  How  estimated,  726. 
Smee's  cell  or  battery,  391. 
Solar  energy,  746 ;  spectrum,  700. 
Soldering,  App.  B. 
Solenoid,  Exp.  101,  p.  315. 
Solid  defined,  54,  61. 
Sonometer,  Fig.  268 ;  519,  App.  Q. 
Sonorous  tubes,  531. 
Sound,  Analysis  of,  Exp.  16,  p.  404; 

529  (a). 
beats,  516,  517. 

"     Cause  of,  483. 

"     defined,  477. 

"     Focus  of,  501. 

u     Interference  of,  515. 

"     media,  486. 

"      Propagation  of,  484. 

"     Quality  of,  528. 

u      Reflection  of,  502-504. 

"     Refraction  of,  500,  501,  516,  517. 

"•     Reinforcement  of,  511-514. 

"     Synthesis  of,  529  (a). 

"     Timbre  of,  528. 

"     Velocity  of,  487-489. 

"     waves.  485. 
Sounder,  Telegraphic,  445  (a). 
Sounding-board,  510. 
Spark,  Electric,  362  ;   Exp.  35,  p.  233; 

46o. 

Speaking-tubes,  495. 
Specific  gravity  defined,  241. 

"  "        of  gases,  248. 

"  "       "  liquids,  242, 246. 

"  u       "  solids,  242  245. 


594 


INDEX. 


Numbers  refer  to  paragraphs,  unless  otherwise  indicated. 


Specific  heat,  596-601. 

"       inductive  capacity,  352. 

"       inductivity,  352. 

resistance  (electric),  App.  K  (2). 
Spectroscope,  703  (b). 
Spectrum,  700,  702,  704,  716-719. 
Spherical  aberration,  698. 
Spouting  liquids,  254-256. 
Sprengel's  air  pump,  290. 
Springs,  Intermittent,  301. 
Stability,  116. 

Standard  candle,  Ex.  5,  p.  482. 
Static  electricity,  see  frictional. 
Steam,  573,  594. 
Steam-engine,  635-643,  App.  S. 
Stereoscope,  735,  736 
Storage  battery,  415. 
Storms,  Thunder,  367.  [p.  252. 

Striking  distance  of  Ley  den  jar,  Ex.  n, 
Stringed  instruments,  530. 
Strings,  Musical,  518,  519. 
Stubs'  wire  gauge,  App.  I. 
Submarine  cables,  359,  360,  App.  L  (3). 
Successive  electric  induction,  335. 
Sunbeam  analyzed,  716-719. 
Surface  electrification,  341. 
Surveyor's  compass,  439  (a). 
Swan  lamps,  466. 
Sympathetic  vibrations,  509,  625. 
Synthesis  of  sound,  529  (a). 
"       "  white  light,  704. 


Tandem  joining  of  cells,  398. 
Tangent  galvanometer,  App.  L  (i). 
Tangents,  Natural,  Table  of,  App.  L 

0). 

Tantalus's  cup,  301. 
Telegraph,  444-446. 
Telegraphic  plant,  445  (c). 

"          relay,  445  (6). 

"          repeater,  445  (d). 

"  sounder,  445  (a). 

Telephone,  468,  469,  505-507,  App.  O. 
Telephonic  transmitter,  507. 
Telescope,  73i-733,  App.  T. 
Temperature,  539,  559- 
Temporary  magnet,  307. 
Tenacity,  48. 
Tension,  Electric,  326. 

"       of  gases,  62,  269,  282-287. 
Terrestrial  magnetism,  437-441. 
"        telescope,  733. 


Testing,  Electric,  App.  M  (i). 
Tests  for  electricity,  322,  323,  417,  418. 
Theory  of  electricity,  337. 
Thermal  effects  of  electric  currept,  406 
"       spectrum,  718. 
"       units,  579. 
Thermodynamics,  626, 

"  First  law  of,  630. 

Thermo-electricity,  311,  374,  419-422. 
Thermo-electric  pair,  420. 
"  pile,  421. 

Thermometers,  541-547,  Aop.  R. 
Thermometric  readings,  546. 

"  scales,  545. 

Thunder  storms,  367. 
Timbre,  528. 
Tin  tree,  Exp.  77,  p.  283. 
Toepler-Holtz  electric  machine,  Note, 

p.  222. 
Tones,  Fundamental,  524,  525. 

"      Musical,  491. 
Torricelli,  274. 

Total  internal  reflection,  68 1. 
Tourmaline  tongs,  740. 
Transferrer,  292. 
Translucent  bodies,  646. 
Transmission  of  power,  Electric,  474. 
of  pressure   by  liquids, 

216. 

Transmitter,  Telephonic,  507. 
Transparent  bodies,  646. 
Trembler,  Electric,  447. 
Triangle  of  forces,  87. 
Tube  of  force,  App.  N. 
Tubes,  Acoustic  or  speaking,  495. 

"      Sonorous,  531. 
Tuning-fork,  510  (^-516,  529. 
Turbine  wheel,  265. 

U 

Ultra-red  rays,  718. 
Ultra-violet  rays,  719. 
Undershot  wheel,  263. 
Undulations,  478. 
Unit  of  electric  capacity,  359. 
"       current,  385. 
"       resistance,  380. 
"       quantity,  387. 
E.  M.  F.,  382. 
force,  68,  69. 
heat,  579- 

matter,  Chemical,  6. 
"       Physical,  5. 


INDEX. 


595 


Numbers  refer  to  paragraphs,  unless  otherwise  indicated. 


Unit  of  power,  155,  475. 

"     "  work,  153,  154. 
Units,  Absolute  (electromagnetic),  451. 
"     C.  G.  S.,  69,  154,  450,  451- 
"     Electric,  320,  321,  329,  330,  359, 

450-452. 

Electromagnetic,  451. 
"      F.  P.  S.,  68. 
"      Magnetic,  450. 
"      Practical  (electromagnetic),  452. 
Universal  discharger,  358. 

"        properties,  18,  20. 
Upward  pressure,  227,  228. 


Vacuum  pan,  571  (a). 
Vapor  defined,  58. 

"     pressure,  568. 

Vaporization  of  water,  Heat  equiva- 
lent of,  594. 
Variation,  Line  of  no,  441. 

"         Magnetic,  441. 
Velocity,  Increment  of,  127. 
"       of  light,  653. 
"       of  molecules,  62  (a). 
"       of  sound,  487-489. 
Vena  contracta,  App.  E. 
Vertical  needle,  439,  440. 
Vibration,  Amplitude  of,  140,  481,  493. 

"         of  pendulum,  140. 
Vibrations,  Sympathetic,  509,  625. 
Violin,  518,  519  (a). 
Vision,  Distinctness  of,  727. 

"      Persistence  of,  725. 
Visual  angle,  652. 
Vocal  apparatus,  535  (a). 
Volt,  382. 
Voltaic  arc,  467. 

"      battery,  398-402. 

"       cell,  306,  375,  390-397. 

*'      current,  375. 

"      electricity,  305,  306,  373-418. 

"      element,  see  cell. 
Volt-ampere,  475. 
Volt-meter,  App.  M  (4*:). 


Volta's  pistol,  Exp.  58,  p.  244. 
"      hail,  Exp.  39,  p.  240. 

W 

Water,  Expansion  of,  553,  554. 

"      Heat    equivalent  of  vaporiza- 
tion of,  594. 

"      Maximum  density  of,  553. 
*'      power,  260. 
"      Specific  heat  of,  601. 
"      voltameter,  410. 
"      wheels,  261-264. 
Watt,  475. 

Wave  length,  480,  482,  499. 
"     period,  479,  482,  498. 
Waves,  Coincident,  511. 

"      Reflected,   Exps.   8  and  9,  p. 

392,  Exp.  ii,  p.  394. 
Wedge  defined,  205. 

"      Use  of,  206,  207. 
Weight,  33,  103. 

"        Law  of,  105. 
Wheatstone's  bridge,  App.  M  (ze). 
Wheel     and     axle,     Advantages     of 

180. 

defined,  179. 

"  "  «'        Forms  of,  184. 

"  "  "        Formulas,  182. 

"  "  "        Law  of,  183. 

Wheel  armature,  464. 
Wheels,  how  connected,  189. 
Wheels,  Water,  261-264. 
Wheel-work,  185-188. 
White  light,  Composition  of,  704. 
Wind  instruments,  530. 
"     power,  App.  H. 
Wire,  App.  I. 
Work  defined,  150. 
"    Unit  of,  153. 


Yellow  spot  of  eye,  724. 


Zero  of  temperature,  Absolute,  558 
Zincs,  Amalgamating,  388. 


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